Answer:
To ensure that they all have the equal amount of power; to make sure one branch doesn't have more power than the others.
You have a bag of poker chips, containing 2 white, 1 red, and 3 blue chips. White chips are worth $1, red chips are worth $3 and blue chips are worth $5. You need $7 worth of chips in order to see someone’s raise, so you take chips out of the bag one at a time, noting the color of each one as it’s removed, and stop when the total value of the chips removed is at least $7. How many sequences of chip colors are possible when you do this?
There are 144 possible sequences of chip colors.
How many sequences of chip colors are possibleWe can solve this problem by counting the number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7.
Let's consider all the possible sequences of chips that can be drawn from the bag. The first chip can be any of the 6 chips in the bag. For each chip color, there are different scenarios that can happen after drawing the first chip:
If the first chip is a white chip, then we need to draw chips worth $6 more in order to reach $7. We can draw any combination of the remaining 5 chips to get a total value of $6 or more. There are 2 white, 1 red, and 3 blue chips remaining, so there are 2^5 = 32 possible combinations.If the first chip is a red chip, then we need to draw chips worth $4 more in order to reach $7. We can draw any combination of the remaining 5 chips to get a total value of $4 or more. There are 2 white, 1 red, and 3 blue chips remaining, so there are 2^5 = 32 possible combinations.If the first chip is a blue chip, then we need to draw chips worth $2 more in order to reach $7. We can draw any combination of the remaining 5 chips to get a total value of $2 or more. There are 2 white, 1 red, and 2 blue chips remaining, so there are 2^4 = 16 possible combinations.Therefore, the total number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7 is: 2 x 32 + 1 x 32 + 3 x 16 = 144
Learn more on sequence here;
https://brainly.com/question/6561461
#SPJ1
Robert picked 65 apples at a local orchard. 26 of the apples were green what PERCENT were NOT green?
Answer: 65-26=39
Step-by-step explanation: because when we have a portion of the apples that are green and the other is not the word problem indicates subraction and since we have both units of the expression already given we get a answer of 39 apples that were not green
if f(r)= 3.14 r^2 what is f(3)
Answer:
f(3) = 28.26
Step-by-step explanation:
Substitute r = 3 into f(r) , that is
f(3) = 3.14 × 3² = 3.14 × 9 = 28.26
(a) Let X denotes the number of bad oranges in a box sold by a hawker. The probability distribution of X is shown below. X = x 0 1 2 3 4 P(X=x) 5k 4k 3k 2k k where k is a constant number. i) Find the value of k, in terms of a fraction. Determine E(X) and Var (X). Illustrate the probability distribution of X in a graph. (10 marks) (b) A factory manufactures 3000 electronic chips every day. It is known that 0.8% of chips are faulty. i) ii) Using an approximation to a normal distribution, find the probability that at least 35 faulty chips are produced in one day. The quality control system in the factory identifies and destroys every faulty chip at the end of the manufacturing process. It costs RM 0.45 to manufacture a chip, and the factory sells non- faulty chips for RM 2.50. Find the expected profit made by the factory per day. (9 marks) (TOTAL: 19 MARKS)
(a) Let's solve part (a) step by step.
i) To find the value of k, we need to use the fact that the sum of probabilities in a probability distribution must equal 1. Therefore, we can set up the equation:
5k + 4k + 3k + 2k + k = 1
Combining like terms, we have:
15k = 1
Dividing both sides by 15, we get:
k = 1/15
So the value of k is 1/15.
ii) To find E(X) (the expected value or mean) and Var(X) (the variance), we can use the formulas:
E(X) = Σ(x * P(X = x))
Var(X) = Σ((x - E(X))^2 * P(X = x))
Using the probability distribution given, we can calculate E(X) and Var(X) as follows:
E(X) = (0 * 5/15) + (1 * 4/15) + (2 * 3/15) + (3 * 2/15) + (4 * 1/15)
= 0 + 4/15 + 6/15 + 6/15 + 4/15
= 20/15
= 4/3
Var(X) = (0 - 4/3)^2 * 5/15 + (1 - 4/3)^2 * 4/15 + (2 - 4/3)^2 * 3/15 + (3 - 4/3)^2 * 2/15 + (4 - 4/3)^2 * 1/15
= (0 - 4/3)^2 * 5/15 + (1/3)^2 * 4/15 + (2/3)^2 * 3/15 + (5/3)^2 * 2/15 + (4/3)^2 * 1/15
= (4/3)^2 * (5/15 + 4/15 + 2/15 + 1/15) + (1/9) * (4/15) + (4/9) * (3/15) + (25/9) * (2/15) + (16/9) * (1/15)
= (16/9) * (12/15) + (4/135) + (12/135) + (50/135) + (16/135)
= (16/9) * (16/15)
= 256/135
So, E(X) = 4/3 and Var(X) = 256/135.
To illustrate the probability distribution of X in a graph, we can plot the values of X on the x-axis and the corresponding probabilities on the y-axis.
(b) i) To find the probability that at least 35 faulty chips are produced in one day, we can use the normal approximation. Since the sample size is large (3000), we can assume the distribution of the number of faulty chips follows a normal distribution.
The mean (μ) of the distribution is given by:
μ = (sample size) * (probability of being faulty) = 3000 * 0.008 = 24
The standard deviation (σ) is calculated using the formula:
σ = sqrt((sample size) * (probability of being faulty) * (1 - probability of being faulty))
= sqrt(3000 * 0.008 * (1 - 0.008))
≈ 5.29
To find the probability of at least 35 faulty chips, we calculate the z-score for 35 using the formula:
z = (x - μ) / σ
z = (35 - 24) / 5.29 ≈ 2.08
Using a standard normal distribution table or calculator, we can find the probability associated with z = 2.08, which represents the probability of at least 35 faulty chips.
ii) To find the expected profit made by the factory per day, we need to consider the cost of manufacturing and the revenue from selling non-faulty chips.
The expected profit per chip is given by:
Profit per chip = Revenue per chip - Cost per chip
Revenue per chip = Selling price per chip = RM 2.50
Cost per chip = Manufacturing cost per chip = RM 0.45
The probability of a chip being non-faulty is 1 - probability of being faulty = 1 - 0.008 = 0.992.
Expected profit per chip = (Revenue per chip) * (Probability of non-faulty chip) - (Cost per chip) * (Probability of non-faulty chip)
= RM 2.50 * 0.992 - RM 0.45 * 0.992
= RM 2.48
Since the factory manufactures 3000 chips per day, the expected profit made by the factory per day is:
Expected profit per day = Expected profit per chip * Number of chips per day
= RM 2.48 * 3000
= RM 7440
Therefore, the expected profit made by the factory per day is RM 7440.
To know more about Probability visit-
brainly.com/question/31828911
#SPJ11
Which best describes why the function is nonlinear? the rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees. the rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
What is a nonlinear function?A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.
The rate of change between 2 and 3 trees is given by:
R₂₃ = (180 - 120)/(3-2)
R₂₃ = 60.
Also, the rate of change between 3 and 5 trees is given by:
R₃₅ = (290 - 180)/(5-3)
R₃₅ = 110/2
R₃₅ = 55.
Read more on nonlinear function here: https://brainly.com/question/896694
#SPJ1
Complete Question:
A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?
The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
What is a nonlinear function?
A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.
The rate of change between 2 and 3 trees is given by:
R₂₃ = (180 - 120)/(3-2)
R₂₃ = 60.
Also, the rate of change between 3 and 5 trees is given by:
R₃₅ = (290 - 180)/(5-3)
R₃₅ = 110/2
R₃₅ = 55.
Read more on nonlinear function here: brainly.com/question/896694
#SPJ1
Complete Question:
A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?
Solve the following system of equations. Show your work.
−2x+5y=−2
4x−10y=4
Solution:
Equations −2x+5y=−2 and 4x−10y=4 have no solution.
Define no solution.An inconsistent system is a set of equations that cannot be solved. Although a system of linear equations typically has a single solution, it occasionally may have infinite or no solutions (parallel lines) (same line). The solution set refers to all possible answers to an equation or inequality. The no solution symbol,, is used to indicate that there is no solution to an equation or inequality. None Found: There are no solutions when the lines that make up a system are parallel because the two lines have no points in common.
Given,
Equations,
−2x+5y=−2 .. Equation 1
4x−10y=4 .. Equation 2
Multiplying equation 1 by 2
-4x + 10y = -4
4x - 10 y = 4
-----------------
0
Equations −2x+5y=−2 and 4x−10y=4 have no solution.
To learn more about no solution, visit:
https://brainly.com/question/7932885
#SPJ1
urgenttttttt
boat rentals are 20 per hour plus a $50 rental fee. This can be expressed with the function C(h) = 20h + 50. If a rental cost $170, how many hours was the boat rented?
in what direction is the derivative of ( ) 2 f x, y = xy − y at the point (3,2) equal to zero? give the answer as a unit vector.
Answer:
To find the direction of the derivative at the point (3, 2) where it is equal to zero, we need to find the gradient of the function at that point and then find a unit vector in that direction.
Taking partial derivatives with respect to x and y, we get:
∂f/∂x = y - 0 = y
∂f/∂y = x - 1
At the point (3, 2), we have:
∂f/∂x = 2
∂f/∂y = 3
So the gradient at that point is the vector <2, 3>.
To find a unit vector in the direction of this gradient, we first calculate its magnitude:
|<2, 3>| = sqrt(2^2 + 3^2) = sqrt(13)
Then we divide the gradient vector by its magnitude:
<2, 3>/sqrt(13) = (2/sqrt(13))i + (3/sqrt(13))j
So the unit vector in the direction of the derivative at the point (3, 2) is (2/sqrt(13))i + (3/sqrt(13))j.
hii! if this helps u! give me thanks and rate 5*~ thankyou!
Explain how to decide which is a better value. 4 greeting cards for $10 and 6 greeting cards for $14.
Answer:
I dont know if this is supposed to be solved a certain way for a class, but as a bargain shopper, this is what I would do to figure out the best value.
Step-by-step explanation:
First divide $10 by 4: 10.00/4=2.5 or $2.50 per card
Then, divide $14 by 6: 14.00/6=2.3333333 so about $2.33 per card
Now, just look at the two answers and see which one is less.
If you buy 4 cards for $10, you will pay $2.50 for each card and if you buy 6 cards for $14, you will pay about $2.33 for each card. Therefore, the better value would be the 6 cards for $14.
FILL IN THE BLANK. Suppose two statistics are both unbiased estimators of the population parameter in question. You then choose the sample statistic that has the ____ standard deviation. O A. larger O B. sampling O C. same OD. least
When choosing between two unbiased estimators of a population parameter, the one with the lower standard deviation is generally preferred as it indicates that the estimator is more precise. The correct answer is option d.
In other words, the variance of the estimator is smaller, meaning that the estimator is less likely to deviate far from the true value of the population parameter.
An estimator with a larger standard deviation, on the other hand, is less precise and is more likely to produce estimates that are farther from the true value. Therefore, it is important to consider the variability of the estimators when choosing between them.
It is worth noting, however, that the standard deviation alone is not sufficient to fully compare and evaluate two estimators. Other properties such as bias, efficiency, and robustness must also be taken into account depending on the specific context and requirements of the problem at hand.
The correct answer is option d.
To know more about standard deviation refer to-
https://brainly.com/question/23907081
#SPJ11
Hello! Can someone help me with this!!
Answer:
nope u dont need to buy more
Step-by-step explanation:
u have 1/2 cup after spilling but the recipe only needs 1/3 which is less
Can someone share points with me like 100 post a question
Answer:
I do have extra points I can give.
Step-by-step explanation:
Can somebody help me plz and thank you
Answer:
sure, what do you need help with?
Step-by-step explanation:
what is 55 degrees in radian measure as a multiple of pi
x/x+2-4/x-2=1
I forgot how to do these types of questions.
Answer:
\(\mathrm{No\:Solution}\)
Step-by-step explanation:
\(\frac{x}{x}+2-\frac{4}{x}-2=1\)
Step 1: Subtract \(2\:-2\) from both sides
\(\frac{x}{x}+2-\frac{4}{x}-2-\left(2-2\right)=1-\left(2-2\right)\\\\\frac{x}{x}-\frac{4}{x}=1\)
x over x is 1
\(1-\frac{4}{x}=1\)
Step 2: Multiply both sides by \(x\)
\(1\cdot \:x-\frac{4}{x}x=1\cdot \:x\\\\x-4=x\)
And when you solve for \(x-4=x\), the answer is \(\mathrm{No\:Solution}\), NOT THERE IS NO SOLUTION.
Evaluate the expression for p = -1.
7p =
Answer:
-7
Step-by-step explanation:
Expression: 7p
Value of p: p = -1
Substitute p in the expression with the value given for p, -1.
Then, multiply by 7.
7p = 7 × (-1) = -7
2. [3pts] In the context of a simple linear regression model y = β0 + estimated by least squares with n observations, show that the LS estimator of βˆ0 is equal to the sample mean of the dependent variable.
3. [4pts] In the context of a simple linear regression model y = β0 + β1x + estimated by least squares with n observations, show that the LS estimator of βˆ1 is βˆ 1 = sample covariance between x and y sample variance ofx Most of the following questions require a proof. Please make sure you mention the assumptions used in your proofs.
The LS estimator of βˆ0 in a simple linear regression model is equal to the sample mean of the dependent variable, while the LS estimator of βˆ1 is equal to the sample covariance between x and y divided by the sample variance of x.
1. LS estimator of βˆ0:
In a simple linear regression model, the equation is y = β0 + ε, where y represents the dependent variable, β0 is the intercept, and ε is the error term. The LS estimator of βˆ0 is obtained by minimizing the sum of squared residuals (SSR). The SSR is defined as the sum of the squared differences between the observed values of y and the predicted values of y based on the model.
When we minimize the SSR, we differentiate it with respect to β0 and set the derivative equal to zero. This leads to the condition that the LS estimator of βˆ0 is equal to the value of β0 that minimizes the SSR. The value of β0 that minimizes the SSR is the one that makes the sum of the residuals equal to zero.
Since the residuals represent the differences between the observed values of y and the predicted values of y, the sum of the residuals can be interpreted as the sum of the deviations of the observed values from the predicted values. When the sum of the residuals is zero, it implies that the sum of the deviations is also zero.
Therefore, the LS estimator of βˆ0 is equal to the sample mean of the dependent variable, as the sample mean represents the average value of the dependent variable and minimizes the deviations from the predicted values.
2. LS estimator of βˆ1:
In a simple linear regression model, the equation is y = β0 + β1x + ε, where y represents the dependent variable, x represents the independent variable, β0 is the intercept, β1 is the slope, and ε is the error term. The LS estimator of βˆ1 is obtained by minimizing the SSR, similar to the LS estimator of βˆ0.
To derive the LS estimator of βˆ1, we differentiate the SSR with respect to β1 and set the derivative equal to zero. This leads to the condition that the LS estimator of βˆ1 is equal to the value of β1 that minimizes the SSR. The value of β1 that minimizes the SSR is the one that makes the sum of the products of the residuals and the corresponding values of x equal to zero.
The product of the residuals and the values of x represents the covariance between x and y, as it measures the joint variability between the two variables. The sum of these products being zero implies that the covariance between x and y is zero.
The sample covariance between x and y divided by the sample variance of x is an unbiased estimator of the population slope β1. Hence, the LS estimator of βˆ1 is given by the sample covariance between x and y divided by the sample variance of x.
Learn more about estimator
brainly.com/question/30876115
#SPJ11
divide the sum of 15 and 16 by 5
Answer:
6.2
Step-by-step explanation:
15+16=31
31/5=6.2
Step-by-step explanation:
\(15 + 16 \div 5 \\ calculate \: the \: sum \: of \: 15 \: and \: 16 \\ 31 \div 5 = 6 \frac{1}{5} \\ or \: 6.2\)
Mr. Stewart wants to cut a board that is 34 inches long into four pieces that are the same length. How long will each
board be after he cuts them?
08.0 inches
8.2 inches
8.4 inches
O 8.5 inches
Please help!!!!!!!!!
Consider this equation.
7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)
Mia solved the equation and determined that m = 2. Is she correct?
She is incorrect because when substituting 2 for m the result was a true statement.
She is incorrect because when substituting 2 for m the result was a false statement.
She is correct because when substituting 2 for m the result was a true statement.
She is correct because when substituting 2 for m the result was a false statement.
Can someone please help me?
Answer:
it's wrong
Step-by-step explanation:
because the answer in this 7.8 + 2(0.75m+ 0.4) is not 6.4
Answer:
B she is incorrect because when substituting 2 for m the result was a false statement
Step-by-step explanation:
i just did it on edge
Sketch the graph of each line.
By determining the x-intercept and y-intercept of the line, the graph of the line is shown below
Graph of a straight lineFrom the question, we are to draw the graph of the given line
From the given information,
The equation of the line is
3x + y = -3
To graph the line, we will determine the x-intercept and y-intercept of the line
Determine the x-intercept
3x + y = -3
Set y = 0
3x + 0 = -3
3x = -3
x = -3/3
x = -1
(-1, 0)
Determine the y-intercept
3x + y = -3
Set x = 0
3(0) + y = -3
y = -3
(0, -3)
Using the x-intercept and y-intercept, the graph of the line is shown below
Learn more on Graph of a straight line here: https://brainly.com/question/29478176
#SPJ1
rove that any abelian group of order 100 has an element of order 10. does every abelian group of order 100 have an element of order 4?
Considering that G is an abelian group of order 100, Cauchy's Theorem suffices in place of Sylow's Theorems: G has an element of order 2 and an element of order 5 since the numbers 2 and 5 divide |G|.
What is and abelian group?
An abelian group, also known as a commutative group in mathematics, is a set of elements where the outcome of performing a group operation on two members of the set does not rely on the order in which the items were written. That is, commutative group operations are possible.
You are required to demonstrate that an element of order 10 must be present in an abelian group G of order 100 in the first portion of the issue. To enumerate the possibilities for H and K in this section, we apply the Sylow theorem. \(|H| = 2^2 and |K| = 5^2\) Since there is no subgroup of order 25, K must be normal, although H may not be since 125 mod 2. I also demonstrated that HK=G and that their sole shared property is the identification element.
If H and K are healthy, that is. G has to be isomorphic to one of the groups listed below:
\(Z_4 X Z_25\\ Z_2 X Z_2 X Z_25\\ Z_4 X Z_5 X Z_5\\ Z2 X Z2 X Z5 X Z5\)
Considering that G is an abelian group of order 100, Cauchy's Theorem suffices in place of Sylow's Theorems: G has an element of order 2 and an element of order 5 since the numbers 2 and 5 divide |G|. Then, a+b=0 (writing the groups additively), and this readily demonstrates that a+b has order 10:
k(a+b)=0
⟺ka+kb=0
⟺ka=−kb
⟺ka,kb∈{0
}⟺2|k and 5|k
⟺10|k.
To know more about abelian group visit:
https://brainly.com/question/15586078
#SPJ4
PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!
A rectangular pyramid has a volume of 216 in³. A rectangular prism has the same height as the rectangular pyramid and a base that is congruent to the base of the rectangular pyramid.
What is the relationship between the volume of the rectangular pyramid and the rectangular prism?
A.The volume of a rectangular prism is 2 times the volume of a rectangular pyramid. The volume of the rectangular prism is 432 in3.
B.The volume of a rectangular prism is 13 the volume of a rectangular pyramid. The volume of the rectangular prism is 72 in3.
C.The volume of a rectangular prism is 12 the volume of a rectangular pyramid. The volume of the rectangular prism is 108 in3.
D.The volume of a rectangular prism is 3 times the volume of a rectangular pyramid. The volume of the rectangular prism is 648 in3.
The relationship between a prism and a pyramid is the volume of a rectangular prism is 3 times the volume of a rectangular pyramid. The volume of the rectangular prism is 648 in3.
What is a rectangular prism?A rectangular prism is a 3-dimensional object. It has six rectangular faces . It has 8 vertices, 6 faces, and 12 edges. The volume of a rectangular prism = width x height x length
What is a rectangular pyramid?A rectangular pyramid is a three-dimensional object. It is made up of a rectangular base and a triangular face. The volume of a rectangular pyramid = 1/3(width x height x length )
To learn more about rectangle pyramid, please check: https://brainly.com/question/9222686
Answer:
It is C
Step-by-step explanation:I Have the exact answer on my test
what are the steps to evaluate an exponential expression
The steps to evaluate an exponential expression include:
Identify the base and the exponent in the expressionReplace the base with the value that you want to use.Use the exponent to determine how many times the base should be multiplied by itself.Perform the multiplication and simplify the expression.How to evaluate an exponential expression ?First, you need to identify the base which is the number being raised to a power, and the exponent is the power to which the base is being raised. Then replace this base with the value that is needed to be used.
Use this exponent such that you can find out the number of times the base will multiply itself and then do the multiplication and simplify the expression.
Find out more on exponential expressions at https://brainly.com/question/5085217
#SPJ1
Solve for k in the following equation:
m =
8kx
7.
- 6
Answer:
m=56kx-6
Step-by-step explanation:
Can anyone help pls I’m struggling on this
Step-by-step explanation:
9311/35. 1/9
plz mark my answer as brainlist plzzzz.hope this will be helpful to you.
☺️
Can someone help me with this math homework please!
9514 1404 393
Answer:
(a) Micah's solution is wrong.
Step-by-step explanation:
After adding 5/2x to both sides, Micah should have obtained ...
5/6 = 8
This would indicate there are no values of x that make the statement true.
Choose the system of equations which matches the following graph.
A. 3x-6y=12
9x-18y=36
B. 3x+6y=12
9x+18y=36
The system of equations that matches the given graph is:
A. 3x - 6y = 12
9x - 18y = 36
To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.
Looking at the options provided:
A. 3x - 6y = 12
9x - 18y = 36
B. 3x + 6y = 12
9x + 18y = 36
Let's analyze the equations in each option:
For option A:
The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.
The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.
In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.
For option B:
The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.
The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.
In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.
for such more question on system of equations
https://brainly.com/question/4262258
#SPJ8
let p (t) = 600(0.974)t be the population of the good place in the year 1900. a) rewrite this equation in the form p(t) = aekt. round k to at least 4 decimal places.
let p (t) = 600(0.974)^t be the population of a good place in the year 1900. a) rewrite this equation in the form p(t) = ae^(kt)
The final form of the given exponential function p(t) = 600(0.974)^t is p(t) = 600e^(-0.0264t).
The exponential function is a mathematical function where an independent variable is raised to a constant, and it is always found in the form y = ab^x. Here, we need to rewrite the given equation p(t) = 600(0.974)^t in the form p(t) = ae^(kt)Round k to at least 4 decimal places.
We know that exponential function is in the form p(t) = ae^(kt)
Here, the given equation p(t) = 600(0.974)^t ... equation (1)
The given equation can be written as:
p(t) = ae^(kt) ... equation (2)
Where,p(t) is the population of a good place in the year 1900
ae^(kt) is the form of the exponential function
600(0.974)^t can be written as 600(e^(ln 0.974))^t
p(t) = 600(e^(ln 0.974))^t
p(t) = 600(e^(ln0.974t) ... equation (3)
Comparing equations (2) and (3), we get: a = 600
k = ln 0.974
Rounding k to at least 4 decimal places, we get k = -0.0264
Therefore, the final form of the given exponential function p(t) = 600(0.974)^t is p(t) = 600e^(-0.0264t)
Learn more about exponential function: https://brainly.com/question/2456547
#SPJ11