The fish population in a local stream is decreasing at a rate of 3% per year. The original population was 48,000. Write an exponential function to model this situation. Then find the population after 7 years.
Answers
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Decrease rate (d)= 7%
Number of periods (n)= 7 years
Current population (PV)= 48,000
First, to calculate the future value, we need to use the following decrease exponential formula:
FV= PV*[(1+d)^-n]
After 7 years:
FV= 48,000*(1.07^-7)
FV= 29,892
The fish population after 7 years is 38783
An exponential decay is in the form:
y = abˣ;
where y, x are variables, a is the initial value of y and b is < 1
Let y represent the fish population after x years.
Since there is initially 48000 fish, hence a = 48000. Also it decrease at a rate of 3% per year. Hence b = 100% - 3% = 97% = 0.97
Therefore:
y = 48000(0.97)ˣ
After 7 years:
y = 48000(0.97)⁷ = 38783
Therefore the fish population after 7 years is 38783
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Related Questions
Mrs. Adesso wants to take her class on a trip to either the science center or natural history museum. The science center charges $8 per student, plus a flat fee of $5 for a group tour. The natural history museum charges $5 per student, plus a flat fee of $20 for a group tour. For what number of students is the cost of the trip the same at each museum?
Answers
The number of students is the cost of the trip the same at each museum is 25
What number of students is the cost?When we write expressions for the total cost of each field visit and set them equal, we find the solution to be the ratio of the difference in fixed cost to the difference in variable cost.
y = 75 +7x . . . . . cost for x students to visit the science center
y = 50 +8x . . . . cost for x students to visit the natural history museum
Subtracting the first equation from the second, we get
0 = -25 +x
25 = x . . . . . add 25; the number of students such that costs are equal
The cost will be the same either place for 25 students.
Here, the fixed cost difference is 75-50=25, and the variable cost difference is 8-7=1. The ratio of these costs is
$25/($1 /student) = 25 students.
This relationship only holds when the higher fixed cost is associated with the lower variable cost. Charges are such that one place caters to larger numbers of students (science center), and one prefers fewer students (natural history museum).
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Using mathematical expressions, for the cost of the trip to be the same at each museum, the number of students must be 5.
What are mathematical expressions?Mathematical expressions combine variables, constants or numbers, and mathematical operators., without the equation or inequality symbols.
Science Center History Museum
Cost per student $8 $5
Fixed cost $5 $20
Let the number of students = x
The total cost at the Science Center = 5 + 8x
The total cost at the History Museum = 20 + 5x
For the cost to be the same at either center:
5 + 8x = 20 + 5x
3x = 15
x = 5
Thus, when the number of students attending either museum is 5, the cost is the same.
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Question 1: The population of Ohio's three largest cities are: Cleveland, 479,459; Columbus, 715,230; and Cincinnati, 367,000. The average population of Ohio's three largest cities is:
a. 520,563
b. 620,563
c. 502,563
d. 602,563
Q2: Mr. Gorski bases each student's grade on 4 tests. On the first 3 tests, Horace scored 84, 93, and 88. What must he score on the final test to make his average 90?
a. 85
b. 88
c. 92
d. 95
Answers
A. 520,563
The answer to question 2:
D. 95
To solve question one, we need to find the average of these three numbers. To do so, we add all three first:
479,459 + 715,230 + 367,000 = 1,561,689
Then, after adding, we can divide our result by three because that is how many numbers were used.
1,561,689 divided by 3 = 520,563
Therefore, the average population of Ohio’s three largest cities is 520,563.
To find the answer to question two, we can start by adding the three numbers we have:
84 + 93 + 88 = 265
Because Horace had two tests where he scored in the eighties, we know that in order to average at least a 90, Horace will need to score either a 92 or a 95. When calculating, we will find that if Horace scores a 92, he will be at an average of 89.25. That means that our only reasonable answer is 95 because we can calculate that:
84 + 93 + 88 + 95 = 360
360 divided by 4 equals 90.
Therefore, scoring a 95 on Horace’s final test will put him right on the dot for an average of 90.
Your final answer is D, or 95. Horace will need to score a 95 on his final test to average out to a 90. If you need any extra help, let me know and I will gladly assist you.
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 22 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
Answers
Answer:
220 cards
Step-by-step explanation:
22/x = 10%/100
100x22= 2200 divided by 10= 220
x=220
22/220 = 10%/100
(I know this is 5 days late but I Hope this helped!)
Help plz ASAP for 20pts
Answers
Answer:
Not sure if this is correct but this is what I found.
area of sector=74.84
radius = 8
angle of sector=?
74.84=1/2×8²×angle of sector
74.84=32 × angle of sector
74.84/32= angle of sector
2.33875=angle of sector
Step-by-step explanation:
Sorry if it is incorrect.
In 2012, gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that random samples of 100 respondents were selected from both vermont and hawaii. From the survey, vermont had 65. 3% who said yes and hawaii had 62. 2% who said yes. What is the value of the sample proportion of people from vermont who exercised for at least 30 minutes a day 3 days a week?.
Answers
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653, which is equivalent to 65.3%.
It is important to note that this value is based on a random sample of respondents and may not necessarily represent the true proportion of the entire population of Vermont who exercise regularly.
To find the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week, follow these steps:
1. Convert the given percentage (65.3%) to a decimal by dividing by 100: 65.3 / 100 = 0.653
2. Multiply the decimal by the number of participants in the random sample (100 respondents): 0.653 * 100 = 65.3
3. Round the result to the nearest whole number to find the number of participants who exercised: 65.3 ≈ 65
4. Divide the number of participants who exercised (65) by the total number of participants in the random sample (100): 65 / 100 = 0.65
This means that out of the 100 participants sampled from Vermont, 65.3 of them answered "yes" to the question of whether they had exercised for more than 30 minutes a day for three days out of the week.
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.65 or 65%.
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Someone please help me PLEASE.
With explanations.
Answers
Answer:
hlo
buddy
msg me on
navneet175285
Step-by-step explanation:
njkmmnu
a cube has a volume of 64cm cubed. What is the area of one face of the cube?
Answers
Answer:
96 cm squared
Step-by-step explanation:
-5x+y=-2
-3x+6y=-12
***PLS SHOW STEPS***
Answers
-5x+y=-2
-3x+6y=-12
Substitute the value of y
Y=-2+5x
-3x+6y-12
Plug in
-3x+6(-2+5x)-12
Solve to get
X=0
And then substitute the value of x (* is a multiplication sign)
Y=-2+5*0
Solve
Y=-2
(X,y)=(0,-2)
what is 4x + 1 = 2x - 5
Answers
Answer:
-3
huhftuoyfuiytfyu98y
the profit realized by the sales of a particular item follows a normal distribution with a mean of $0.5 million per quarter and a standard deviation of $0.1 million per quarter. what percent of the quarters can be expected to see a profit of at least $0.5 million?
Answers
98% of the quarters can be expected to see a profit of at least $0.5 million.
What is a standard deviation?
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Z score = 0.7-0.5 = 0.2
σ = 0.1
P-value from Z-Table:
P(x<0.5) = 0.97725
≈ 98%
Hence, 98% of the quarters can be expected to see a profit of at least $0.5 million.
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Lena skied downhill at a steady speed on a 3-mile slope
Answers
Answer:
what are you asking could you clarify, please
Step-by-step explanation:
Answer:
Which fraction represents Lena's speed in miles per hour?
Answer = 3 / 1/4 (three over one fourth)
What is Lena's speed in miles per hour?
Answer = 3 / 1/4 = 12 (three over one fourth equals twelve)
Step-by-step explanation:
i did it on iready and got it right c:
Use Simpson's Rule with n = 6 to estimate the arc length of the curve, L. Give your answer to six decimal places.
x = y + √y, 2≤y≤ 5
Answers
The correct answer is : L ≈ 5.450677 (to six decimal places). The arc length of the curve using Simpson's Rule with n = 6, we first need to find the formula for arc length: L = ∫[a,b] √(1 + (dy/dx)^2) dx
where a and b are the limits of integration, and dy/dx is the derivative of y with respect to x.
To use Simpson's Rule, we divide the interval [2,5] into three subintervals of equal width: h = (5-2)/3 = 1
Then, we can use the following formula: L ≈ h/3 [f(a) + 4f(a+h) + 2f(a+2h) + 4f(a+3h) + 2f(a+4h) + 4f(b)]
where f(x) = √(1 + (dy/dx)^2) and a = 2, b = 5.
To evaluate f(x) and its derivative, we first need to find y as a function of x: x = y + √y → y = x^2 / (4+x)
Then, we can find dy/dx: dy/dx = (2x) / (4+x)^2
Using these formulas, we can calculate f(x) and f'(x) for each x in the interval [2,5]:
f(2) = √(1 + (dy/dx)^2) ≈ 1.03412
f(3) = √(1 + (dy/dx)^2) ≈ 1.06078
f(4) = √(1 + (dy/dx)^2) ≈ 1.09607
f(5) = √(1 + (dy/dx)^2) ≈ 1.14270
Using these values in the formula for Simpson's Rule, we get:
L ≈ 1/3 [1.03412 + 4(1.06078) + 2(1.09607) + 4(1.14270) + 2(1.09607) + 4f(5)]
≈ 5.541921
Therefore, the estimated arc length of the curve L is approximately 5.541921 units, rounded to six decimal places.
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Jake fills a tank that can hold 200 gallons of water. The tank already has 50 gallons of water in it when Jake starts filling it at the rate of 10 gallons per minute. Karla fills a tank that can hold 300 gallons of water. That tank already has 100 gallons of water in it when Karla starts filling it at the rate of 5 gallons per minute. Jake and Karla start filling the tanks at the same time. How long after they start filling the tanks do the tanks have the same volume of water? What is that volume of water? I
Answers
Answer:
Let m represent the number of minutes.
Amount of water in Karla's tank: 100 + 5m
Amount of water in Jake's tank: 50 + 10m
Same amount of water: 100 + 5m = 50 + 10 m
---> 100 = 50 + 5m
---> 50 = 5m
---> 10 = m
In ten minutes, Karla's tank will have 100 + 5(10) = 100 + 50 = 150 gallons.
In ten minutes, Jake's tank will have 50 + 10(10) = 50 + 100 = 150 gallons.
Step-by-step explanation:
hope this helped!
If y varies directly as x, and y = 15 when x = 5. Find x when y = 9
Answers
Answer:
x=3
Step-by-step explanation:
If y is 15 when x is 5, and y =f(x), then the equation is y=3x. Substitute in 9 for y, and do the algebra, and you will get 3. Hope this helped :D
The value of x is 3 when y = 9.
What is Proportionality?When two quantities are proportional, it means that they can be expressed as a ratio or a fraction, and this ratio remains constant as the values of the quantities change.
If y varies directly as x, it means that the ratio of y to x remains constant.
We can express this relationship as y = kx, where k is the constant of variation.
To find the value of k, we can use the given information that y = 15 when x = 5:
15 = k . 5
Dividing both sides of the equation by 5, we get:
k = 15/5
k = 3
Now that we have the value of k, we can substitute it into the equation
y = kx to find x when y = 9:
9 = 3x
Dividing both sides of the equation by 3, we get:
x = 9/3
x = 3
Therefore, when y = 9, x = 3.
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someone help me please with this algebra problem
Answers
Answer:
4
Step-by-step explanation:
3r = 10 + 5s
r = 10
3(10) = 10 + 5s
30 = 10 + 5r
20 = 5r
r = 4
HELP, WILL MARK BRANLIEST
The graph shown represents which of the following polar equations?
Answers
Answer:
the person in the comments was right :)
Step-by-step explanation:
The graph shown represents r= 2+ 5 cos \(\theta\).
What is polar equations?A polar equation is any equation that describes a relation between r and θ, where r represents the distance from the pole (origin) to a point on a curve, and θ represents the counter clockwise angle made by a point on a curve, the pole, and the positive x-axis.
The graph for r=2+ 5 cos \(\theta\) shows the correct formation of the given graph.
the polar equation r=2+ 5 cos \(\theta\) shows the given graph as attached below having range 0 ≤ \(\theta\) ≤2π.
Similarly, the graph for
the polar equation r=4+ 3 sin \(\theta\), the polar equation r=5 cos(3 \(\theta\) ), the polar equation r=3 + 3 cos \(\theta\) is also attached below.
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a group of students carried out a density experiment for an nacl solution and found the following: mean (xm) = 1.060 g/ml, standard deviation (sx) = 0.00773 g/ml, number of measurements = 6.
the literature value for the density based on the known concentration of nacl is 1.071 g/ml.
is there a significant difference for these two values at the 95% confidence level?
Answers
No, there is not a significant difference between these two values at the 95% confidence level.
The difference between the mean and literature values is 0.011 g/ml, which is less than the standard error of the mean (0.00387 g/ml). Therefore, the difference is not statistically significant. To reach a 95% confidence level, the difference must be greater than two standard errors of the mean. This would mean that the difference must be greater than 0.00773 g/ml, which it is not. Therefore, there is no significant difference between these two values at the 95% confidence level.
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Look at the angle. Which description is true
Answers
Answer:
The angle is greater than 90 degrees, which is also known as an obtuse angle.
solve(X+3) (2x-3)-6x=(x-4) (2x+4)+12
Answers
Answer:
5
Step-by-step explanation:
x(2x-3)+3(2x-3)-6x=x(2x+4)-4(2x+4)+12
2x^2-3x+6x-9-6x=2x^2+4x-8x-16+12
2x^2-3x-9=2x^2-4x-4
-3x+4x=-4+9
x=5
Question 1(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
A soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.
28.26 gallons
113.04 gallons
211.38 gallons
845.54 gallons
Question 2(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
A cylinder has a volume of 1 and one sixteenth in3 and a radius of one fourth in. What is the height of a cylinder? Approximate using pi equals 22 over 7.
119 twelfths inches
119 over 22 inches
119 over 44 inches
119 over 56 inches
Question 3(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
What is the volume of a right circular cylinder with a diameter of 6 meters and a height of 14 meters. Leave the answer in terms of π.
504π m3
396π m3
126π m3
84π m3
Question 4(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
What is the volume of the cylinder? Round to the nearest hundredth and approximate using π = 3.14.
cylinder with a segment from one point on the circular base to another point on the base through the center labeled 2.6 feet and a height labeled 4.4 feet
23.35 cubic feet
35.92 cubic feet
71.84 cubic feet
93.4 cubic feet
Question 5(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
Coins are placed into a treasure chest, and each coin has a radius of 1.4 inches and a height of 0.0625 inches. If there are 230 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
0.38 in3
126.39 in3
353.88 in3
88.47 in3
Question 6(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
A helium tank shaped like a cylinder has 2,401π in3 of space inside the tank. If the diameter of the helium tank is 14 inches, what is its height?
49 inches
28 inches
12.25 inches
7 inches
Question 7(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
Bradenton Bakery is baking a cake for a customer's quinceañera. The cake mold is shaped like a cylinder with a diameter of 12 inches and height of 8 inches.
Which of the following shows a correct method to calculate the number of cubic units of cake batter needed to fill the mold? Approximate using pi equals 355 over 113.
V equals 355 over 113 times 12 squared times 8
V equals 355 over 113 times 6 squared times 8
V equals 355 over 113 times 8 squared times 6
V equals 355 over 113 times 8 squared times 12
Answers
After answering the given query, we can state that Thus, the correct equation response is (C) 211.38 liters.
What is equation?In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. Through a mathematical statement, algebraic equations show that two mathematical expressions are equal. For instance, the equal sign separates the numbers 3x plus 5 and 14 in the equation 3x + 5 = 14. To comprehend the relationship between the two lines written on the opposing edges of a letter, use a mathematical formula. The logo and the specific program tend to correspond most of the time. An illustration would be 2x - 4 = 2.
Using the equation V = r2h, where r is the radius and h is the height, one can calculate the capacity of the water cooler. The cylinder has a 3 foot circumference, making its radius 1.5 feet. The sphere stands 4 feet tall.
V is equal to (1.5)2(4) = 28.26 cubic feet.
The water refrigerator holds about 7.48 cubic feet of water, so when it is fully filled, it holds the following amount of water:
7.48 times 28.26 = 211.38 liters.
Thus, the correct response is (C) 211.38 liters.
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What is the correct notation for a function that has any given input value equal to its output value?
A.
f(x) = f(x)
B.
f(x) = x
C.
f(x) = –x
D.
f(x) = 1
Answers
Answer:
0ption B is correct
ie:f(x) = x
Answer:
option B
Step-by-step explanation:
f(X) = x
is the answer
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Answers
Answer:
Wow u good and thanks for the points and I love your profile picture
Step-by-step explanation:
Answer:
wE nEeD cRoNa tO DiE
Step-by-step explanation:
A recent high school graduate received $800 in gifts of cash from friends and relatives. In addition, he received three scholarships in the amounts of $450, $600, $1300. If he takes all his gifts and scholarship money and invests it in a 36-month CD paying 4% interest compound daily, how much will the graduate have when he cashes in the CD at the end of the 36-months?
Answers
Given:
a.) A recent high school graduate received $800 in gifts of cash from friends and relatives.
b.) In addition, he received three scholarships in the amounts of $450, $600, $1300.
We will be using the Compound Interest Formula:
\(\text{ A = P(1 + }\frac{r}{n})^{nt}\)Where,
A = accumulation (the amount of money accumulated after n years with interest)
P = principal (the initial amount you borrow or invest)
r = annual interest rate (in decimal)
n = the number of times the interest is compounded per year
t = the number of years the amount is borrowed or invested for
P = gifts + scholarships = 800 + 450 + 600 + 1300 = $3,150
r = 4% = 4/100 = 0.04
n = daily = 365
t = 36 months = 36/12 = 3 years
We get,
\(\text{ A = P(1 + }\frac{r}{n})^{nt}\)\(\text{ = (3,150)(1 + }\frac{0.04}{365})^{(365)(3)}\)\(\text{ = (3,150)(}1\text{ + }0.00010958904)^{1,095}\)\(\text{ = (3,150)(}1.00010958904)^{1,095}\)\(\text{ = (3,150)(}1.12748943847)\)\(\text{ = }3,551.59173117\)\(\text{ A }\approx\text{ \$}3,551.59\)Therefore, the answer is $3,551.59
De los tres cuartos de los asientos que hay en un camión, quitamos la tercera parte y aun quedan 20. ¿Cuántos asientos tiene el camión?AYUDAA
Answers
Creo que habría 80 asientos.
Last week, you finished Level 2 of a video game in 32 minutes. Today, you finish Level 2in 28 minutes. What is your percent of change
Answers
Answer:
12.5% decrease
Step-by-step explanation:
[(V2 - V1) / V1] x 100 = Percent Change
1) Suppose (a,b) is a multiple of (c,d) and abcd≠0. Show (a,c) is a multiple of (b,d). Using matrices, what does this tell us?2) What 2x2 matrix acts on (x,y) to produce (y,x)?
Answers
The 2x2 matrix that acts on (x,y) to produce (y,x) is the matrix:
[ 0 1 ]
[ 1 0 ]
Suppose (a,b) is a multiple of (c,d) and abcd ≠ 0, then there exists a scalar k such that (a,b) = k(c,d).
Then,
ac = kcd
and
ad = kbd
So,
(a,c) = (ac, ad) = (kcd, kbd) = k(cd, bd) = k(c,b)
Therefore, (a,c) is a multiple of (b,d).
Using matrices, this tells us that if two vectors (a,b) and (c,d) are proportional, then the transpose of either vector is proportional to the other.
The 2x2 matrix that acts on (x,y) to produce (y,x) is the matrix:
[ 0 1 ]
[ 1 0 ]
This is known as the transpose matrix and can be denoted as A^T.
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how would you solve this equation?
Answers
Answer:
19,188
Step-by-step explanation:
hope this helps ;)
If the line px -5y = 60 has a slope of -23 then p equals ....
Answers
Answer:
p = - 115
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
px - 5y = 60 ( subtract px from both sides )
- 5y = - px + 60 ( divide all terms by - 5 )
y = \(\frac{1}{5}\) px - 12 ← in slope- intercept form
with slope m = \(\frac{1}{5}\) p , thus
\(\frac{1}{5}\) p = - 23 ( multiply both sides by 5 to clear the fraction )
p = - 115
What is the slope of the line that passes through the points (-9, -9) and (-9, -7) Write in simplest form.
Answers
Answer:
Undefined slope, vertical line
Step-by-step explanation:
Slope = \(\frac{y_{2} -y_{1}}{x_{2}-x_{1}}\)
Slope = \(\frac{-7 -(-9)}{-9-(-9)} = \frac{-7+9}{-9+9} =\frac{2}{0}\) = Undefined
Since the slope is undefined, you would have a vertical line.
Graph the inequality in a coordinate plane. -X+4y>-12
Need help!!!
Answers
Answer:
Step-by-step explanation:
THE DARK IS GONNA BE RIGHT OVER LEWFT TO PLAY THE Gme