The following data represent (hypothetical) energy consumption normalized to the year 1900. Plot the data. Test the model Q = ae^bx by plotting the transformed data. Estimate the parameters of the model graphically. x
0 10 20 30 40 50 60 70 80 90 100 Year
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Consumption Q
1.00 2.01 4.06 8.17 16.44 33.12 66.69 134.29 270.43 544.57 1096.63 Make an appropriate trunsformation to fit the model P aeh using Equation (3.4). Estimate a and h

Answers

Answer 1

The correct value of a or initial amount in exponential growth \(Q = ae^b^x\) is 789.

Quantity rises over time through a process called exponential growth and it happens when the derivative, or instantaneous rate of change, of a quantity with respect to time is proportionate to the original quantity.

Given that, hypothetical energy consumption normalized to the year 1990 we have to estimate a and h

\(Q = ae^b^x\)

\(ln Q= ln a+bx\)

For the year 1990:
\(x = 0\)     \(lnQ =0\)

For the year 1910:

\(x= 10\)    \(lnQ= 0.698\)

For the year 1920:

\(x=20\)    \(lnQ= 1.4012\)

For the year 1930:

\(x=30\)     \(lnQ=2.1\)

For the year 1940:

\(x=40\)     \(lnQ=2.8\)

For the year 1950:

\(x=50\)     \(lnQ=3.5\)

For the year 1960:

\(x=60\)     \(lnQ=4.2\)

For the year 1970:

\(x=70\)     \(lnQ=4.9\)

For the year 1980:

\(x=80\)     \(lnQ=5.6\)

For the year 1990:

\(x=90\)     \(lnQ=6.3\)

For the year 2000:

\(x= 100\)     \(lnQ= 7\)

Here, estimate the parameters of the model graphically, the slope of line is approximated as follows:

a = \(\frac{1096.63-544.57}{7-6.3}\)

a = \(\frac{552.06}{0.7}\)

a = 788.657

a ≈ 789

Hence, a or initial amount in exponential growth \(Q = ae^b^x\) is 789.

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Related Questions

At a coffee shop, the first 100 customers' orders were as follows. Medium Lange 48 22 What is the probability that a customer ordered a hot drink given that he or she ordered a large? P( Hot | Large) = [ ?) Round to the nearest hundredth​

At a coffee shop, the first 100 customers' orders were as follows. Medium Lange 48 22 What is the probability

Answers

Answer: 0.81 or 81%

Step-by-step explanation:

     We are looking for the probability that the customer ordered a hot drink if they ordered a large one. This means that our whole is 27, since 22 Hot Large + 5 Cold Large = 27 total large drinks.

     To find the probability, we will divide the total number of wanted outcomes by the total number of possible outcomes.

\(\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{hot large drink}}{\text{large drink}} =\frac{22}{27} =0.81\text{ or } 81\%\)

which expressions represents 15 more than the product 6 and 8



Please i need help ​

Answers

Answer:

x-15 = 48

or

x= 15 + (6*8)

Step-by-step explanation:

Pls vote as brainliest

Hi,

The correct answer is x=15 + (6x8)

A line passes through the points (1, 4) and (3 -4). Which is the equation of the line?

A line passes through the points (1, 4) and (3 -4). Which is the equation of the line?

Answers

Answer:

Step-by-step explanation:

(-4 - 4)/(3 - 1)= -8/2= -4

y - 4 = -4(x - 1)

y - 4 = -4x + 4

y = -4x + 8

answer is option 1

The equation -7(u-3) = 70 is solved in several steps below.
For each step, choose the reason that best justifies it.

Answers

Answer:

Etymology ois teh acrorect anwser becuae it sues the rosdws

Step-by-step explanation:

Cuantos yenes se pueden comprar con 200 pesos mx ? si los yenes cuestan 0.178 centavos ayuda rapido

Answers

Usando proporciones, hay que con 200 pesos mx se pueden comprar 0.0645 yenes.

¿Qué es una proporción?

Una proporción es una fracción de la cantidad total, y puede ser encontrada por intermedio de una regla de tres.

En este problema, hay que un yene cuesta $0.17, enquanto $1 = 3100 pesos. Por eso, cada yene es equivalente a 3100 pesos.

Por eso, la regla de tres es:

1 yene - 3100 pesos

x yenes - 200 pesos

Aplicando multiplicación cruzada:

\(3100x = 200\)

\(x = \frac{200}{3100}\)

\(x = 0.0645\)

Con 200 pesos mx se pueden comprar 0.0645 yenes.

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The area of a rectangle is 48 square inches. The length is 98 inches. Write an equation that can be used to find the width of the square.

Answers

Answer:

48 = 98x   (where x is the width)

Step-by-step explanation:

Area of a rectangle = length × width

Let x = width

Given:

area = 48 in²length = 98 in

⇒ 48 = 98x

Answer:

x=0.4897599184

Step-by-step explanation:

→Solution,

Area(A)=48 in²

Lenght(l)=98in

Breadth(b)=?

Let the breadth be x.

As we have,

Area of rectangle=l×b

48 in²=98 in × x

48 in²/98 in = x

x=0.4897599184

Please Help 50 POINTS!!

Please Help 50 POINTS!!

Answers

Answer:

D. \(\frac{(x-7)^2}{8^2} -\frac{(y-2)^2}{7^2}\)

Step-by-step explanation:

hope this helps

Answer:  D has the largest perimeter

Step-by-step explanation:

The top numbers of fractions describe the vertex and  the bottom number square rooted tells you how long each or wide each part of the asymptote rectangle is.

A.

P = 2(11) + 2(3)

P = 22+6

P=28

B.

P = 2(4) + 2(9)

p = 8 +18

P = 26

C.

P = 2(5) + 2(9)

P = 10 +18

P = 28

D.

P =  2(8) + 2(7)

P = 16 +14

P = 30

help me plsssssssss ​

help me plsssssssss

Answers

Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

please help will mark as brainlist

please help will mark as brainlist

Answers

Answer:

176

Step-by-step explanation:

Answer:

\(m\)∠STV = 43°

Step-by-step explanation:

It has the corresponding relation with ∠UTV

Suppose that when Emma was born, her grandparents deposited $20,000 into an account paying 5% interest compounded quarterly. What will the balance be when Emma turns 18? Round to the nearest cent

Answers

Answer: The balance when Emma turns 18 = $ 48,132.38

Step-by-step explanation:

When interest is compounded quarterly, the accumulated amount after t years will be :

\(A= P(1+r)^t\)

, where P =  principal, r= rate of interest( in decimal)

Given: P= $ 20,000 , r= 5% =0.05

t = 18 years

\(A = 20000(1+0.05)^{18}\\\\= 20000(1.05)^{18}\\\\= 20000(2.406619)\\\\=\$\ 48,132.38\)

The balance when Emma turns 18 = $ 48,132.38

can someone explain

can someone explain

Answers

Answer:

K = -2

Step-by-step explanation:

K represents the y-intercept, which is where the line crosses the y axis. We can see from the y = -4x -2, that -2 is the y-intercept, because in y =  mx + b, b is the y -intercept.

~theLocoCoco

at a raffle, 500 tickets are sold at $1 each for three prizes of $100,$50,$10. Find the expected gain or loss for each participant

Answers

The expected gain or loss for each participant is -$0.50, which means that on average, each participant can expect to lose 50 cents for every raffle ticket purchased.

How to find the expected loss or gain for each participant?

To find the expected gain or loss for each participant, we need to calculate the expected value of the raffle ticket.

The probability of winning the first prize of $100 is 1/500, the probability of winning the second prize of $50 is also 1/500, and the probability of winning the third prize of $10 is 1/500. The probability of not winning any prize is (500-3)/500 = 497/500.

The expected value of the raffle ticket can be calculated as:

(expected value of first prize) + (expected value of second prize) + (expected value of third prize) + (expected value of no prize)

= (1/500)($100) + (1/500)($50) + (1/500)($10) + (497/500)($0)

= $0.50

Therefore, the expected gain or loss for each participant is -$0.50, which means that on average, each participant can expect to lose 50 cents for every raffle ticket purchased.

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Prove that, for a, b, and c ∈ Z, a > b and c > 0 =⇒ ac
> bc (part 3 of Proposition 2)

Answers

Our assumption is false

We can prove this statement by contradiction. Suppose a > b and c > 0 but ac < bc.

Since a > b, then a - b > 0. Multiplying both sides by c > 0 gives (a - b)c > 0.

We can then add bc to both sides to get (a - b)c + bc > bc.

Since we assumed that ac < bc, then (a - b)c < 0, and thus (a - b)c + bc < bc, which contradicts the previous result.

Therefore, our assumption is false, and we can conclude that for a, b, and c ∈ Z, a > b and c > 0 =⇒ ac ≥ bc.

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Find and simplify the derivative of the following functions. (a) f(x)=((3/4)x^4+ex^2+π)(x^(3/2)+2/x) (b) f(x)=(3xe^X)/(X^3-1) ​

Answers

(a) To find the derivative of the given function, we need to use the product rule of differentiation first, followed by the chain rule.

Using the product rule, we get;` f(x) = ((3/4)x^4+ex^2+π)(x^(3/2)+2/x)`

We can also write this as;` f(x) = u(x) * v(x)`

where u(x) = (3/4)x^4+ex^2+πand v(x) = x^(3/2)+2/x

Now, using the product rule of differentiation, we get;` f'(x) = u'(x)v(x) + v'(x)u(x)`

where u'(x) and v'(x) are the derivatives of u(x) and v(x) respectively.

We have; u'(x) = 3x^3 + 2ex and v'(x) = (3/2)x^(1/2) - 2/x^2

Thus,` f'(x) = (3x^3 + 2ex)(x^(3/2) + 2/x) + ((3/2)x^(1/2) - 2/x^2)((3/4)x^4 + ex^2 + π)`

Now, simplifying the above expression, we get;` f'(x) = (3/2)x^5 + 2ex^2 + 3πx^(1/2) + 2/x^2 + 6x^(3/2) - 2ex/x^2`

We can further simplify this by combining the like terms to get;` f'(x) = (3/2)x^5 + 2ex^2 + 3πx^(1/2) + 6x^(3/2) + (2/x^2 - 2ex/x^2)

We can simplify the last two terms by taking the common denominator, and get;` nf'(x) = (3/2)x^5 + 2ex^2 + 3πx^(1/2) + 6x^(3/2) + 2(x - e)/(x^2)`

Thus, the required derivative of the function `f(x) = ((3/4)x^4+ex^2+π)(x^(3/2)+2/x)` is `(3/2)x^5 + 2ex^2 + 3πx^(1/2) + 6x^(3/2) + 2(x - e)/(x^2)`

(b) To find the derivative of the given function, we can use the quotient rule of differentiation.

Using the quotient rule, we get;` f(x) = (3xe^X)/(X^3-1)`

We can also write this as;` f(x) = u(x) / v(x)`where u(x) = 3xe^Xand v(x) = X^3 - 1

Now, using the quotient rule of differentiation,

we get;` f'(x) = (u'(x)v(x) - v'(x)u(x)) / (v(x))^2`

where u'(x) and v'(x) are the derivatives of u(x) and v(x) respectively.

We have; u'(x) = 3e^x + 3xe^xandv'(x) = 3x^2Thus,`f'(x) = ((3e^x + 3xe^x)(X^3 - 1) - 3x^2(3xe^x)) / (X^3 - 1)^2`

Simplifying the above expression, we get;` f'(x) = (3e^x(X^3 - 1) - 9x^2e^x) / (X^3 - 1)^2`

Thus, the required derivative of the function `f(x) = (3xe^X)/(X^3-1)` is `(3e^x(X^3 - 1) - 9x^2e^x) / (X^3 - 1)^2`.

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Which is the answer ?! Please help

Which is the answer ?! Please help

Answers

D. Hope this helps 13.9027 :)

The ratio c : g is 2 : 3 and the ratio g : t is 5: 4. Write the ratio c: g: t in its simplest form.​

Answers

The ratio c:g:t in its simplest form is 10/3 : 5 : 4.

The ratio of c:g is 2:3 and the ratio of g:t is 5:4.

To write the ratio c:g:t in the simplest form, we need to express c,g and t in terms of a common value and simplify.

Let's begin;Let g be a common value between the ratios c:g and g:t. We can express c and t in terms of g as;

The ratio of c:g is 2:3. That means c is 2/3 of g.The ratio of g:t is 5:4.

That means t is 4/5 of g.We can now express the ratio c:g:t in terms of g, as;

c:g:t = 2/3 : 1 : 4/5

Multiplying by 15 (the LCM of 3 and 5) to get rid of the fractions, we have;

c:g:t = 10 : 15 : 12

Simplifying, we can divide each term by 3 to get the simplest form of the ratio;c:g:t = 10/3 : 5 : 4

Therefore, the ratio c:g:t in its simplest form is 10/3 : 5 : 4.

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the radius of the earth - the distance from surface to core - is 6,370 kilometers. the planet neptune is 24,620 kilometers. if a scale model of the earth is drawn with a radius of 2.5 centimeters, how large would a scale model of neptune have to be drawn? group of answer choices 9848 cm 9.7 cm 2548 cm 0.02548 cm 3.86 cm

Answers

We may build up a proportion and solve for the scale model radius of Neptune using the ratio between the radii of the two planets and the known scale model radius of the Earth. The scale model of Neptune that is produced has a radius of around 9.7 cm.

We may take advantage of the fact that the ratio between the two planets' radii and the ratio between their respective scale model radii is the same. Let's name the Neptune scale model radius "r" Then, we may set up the ratio shown below:

Neptune's radius is equal to the product of Earth's radius and its scale model.

With the provided values, we may simplify and obtain:

24620 km / 6370 km equals 2.5 cm / r

We obtain the following when solving for "r":

r = (24620 km * 2.5 cm) / (6370 km)

r ≈ 9.7 cm

Therefore, a scale model of Neptune would have to be drawn with a radius of approximately 9.7 cm.

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One manufacturer boxes screws so that each box weighs the same no matter what size the screws are. The graph shows the amount of allowed weight remaining in a given shipment depending on the number of boxes of screws already included.

Answers

Answer:

We need the graph to solve.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the maximum weight allowed in a shipment

YOU GET BRAINLIEST IF YOU HAVE THE BEST PICK UP LINE ;))
LOL (free pfp)

YOU GET BRAINLIEST IF YOU HAVE THE BEST PICK UP LINE ;))LOL (free pfp)
YOU GET BRAINLIEST IF YOU HAVE THE BEST PICK UP LINE ;))LOL (free pfp)

Answers

Answer:

There is something wrong with my cell phone. It doesn't have your number in it.

Step-by-step explanation:

cheesy

pick up line lol

Answer:

Me: You wanna hear a pickup line

Chuckie: sure

Me: Its cheesy ;)

b - 1/4 = 3 1/2 find the variable and explain how to got the answer please thanks

Answers

Answer:

b - 1/4 = 3 1/2

Step-by-step explanation:

b - 1/4 = 3 1/2

b - 1/4 = (3 + 1/2)

4b = 15

b = 15/

4

= 3.75

a survey among tenants of shared apartments asked each tenant what percentage of the cleaning around the apartment he or she does. the survey found that aggregating the percentages for each apartment produces an average of much more than 100%. this result may be due to what bias?

Answers

The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

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determine by how many orders of magnitude the quantities differ. a $100 bill and a dime.

Answers

A $100 bill and a dime differ by a magnitude of 3.

Orders of magnitude can be used in order to define large quantities efficiently and more easily. A dime is a currency used in the US that is equivalent to 0.10 dollars.

So we can represent a dime as 10-¹ of a dollar

and we can write 100 dollars as 10² of a dollar.

Therefore the difference in the order of magnitude of 100 dollars and a dime would be the difference between the powers or exponents of those two quantities,

That is,

2-(-1) = 3

So, the dollar differs by a magnitude of 3 from a dime.

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Find the shaded area below.

Help me

Find the shaded area below. Help me

Answers

Answer:

120^2 cm

Step-by-step explanation:

15•2=30•2=60

21-6=15

15•2= 30•2=60

Let f(x)=√x with f:R→R. Discuss the properties of f. Is it injective, surjective, bijective, is it a function? Why or why not? Under what conditions change this?Explain using examples.I'm having some trouble figuring out this equation.

Answers

The function f(x)=√x with f:R→R is injective and surjective but not bijective.

Injective (or one-to-one): f(x) is injective, which means that if f(x1) = f(x2), then x1 = x2. In other words, if the square root of x1 is equal to the square root of x2, then x1 and x2 are equal.

Surjective (or onto): f(x) is surjective, which means that for every y in the codomain (R), there exists an x in the domain (R) such that f(x) = y. In other words, the square root of any real number can always be expressed as a real number.

Bijective: f(x) is not bijective. The square root function is not bijective because it is not defined for negative values of x.

Function: A function f is a function if for every x in the domain of f, there is exactly one y in the codomain of f such that f(x) = y. In other words, each x in the domain is mapped to exactly one y in the codomain.

In the case of f(x) = √x, it is a function. For every x in the domain of f, which is [0,∞), there is exactly one y in the codomain of f, which is [0,∞), such that f(x) = y.

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.
Simplify 1826.00 - 338.12.​

Answers

Answer:

1487.88

Step-by-step explanation:

Because you have to line the decimals up to make sure you have the correct answer

Harper runs 2200 meters in 10 minutes. How many meters can Harper run in one minute?

Answers

Answer: 220 meters in 1 minute

Step-by-step explanation:

if harper can run 2200 meters in 10 min then that means you can run 220 in 1 min

2200/10 = 220

Answer:

220

Step-by-step explanation:

2200/10 is 220

Hannah's soccer team is trying to raise $4,048 to travel to a tournament in Florida, so they decided to host a pancake breakfast. Each person must pay $23 for the breakfast. How many people need to attend their breakfast in order to raise $4,048?

Answers

The equation would be 23p = 4048. Dividing both sides by 23, p = 176. Of course, there’s no mention the cost per meal to deduct.

Find the value of a in the following figure:
A
B
55°
to
35%
C
D

Answers

Answer:

there is no diagram please add the diagram

what is –0.025 as a fraction.

Answers

Answer:

25/1000

Step-by-step explanation:

you will count the decimals out and divide it by the number of times you used by ten

A tv is sold for ra 10350 with 15% profit. Find the cp of tv

Answers

CP=SP*100÷100+P

so,

CP=10350*100÷100+15

CP=9000

Answer:

solution

Step-by-step explanation:

Let.the cp of TV be RS X

now,CP=SP-profit

or, CP=SP-profit% of Cp (as profit amount =profit % of Cp)

or, x=Rs 10350-15÷100× X

or, x= Rs 10350 _ 3X ÷20

or, x+3x ÷20 =Rs 10350

or, 23x ÷20 = Rs 10350

or, x = 10350×20 divided by 23

Therefore X =Rs 9000

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