Question 1

Find the derivative of

Accepted Answer

D

Question 2

Find the derivative of  .

Accepted Answer

A

Question 3

The population of Aurora, a Nevada ghost town, can be modeled as  where output is measured in people and t is the number of years since 1859. Write a model for the rate of change of the population of Aurora.

Accepted Answer

A

Question 4

Find the derivative of  .

Accepted Answer

The answer of Find the derivative of  .
...

Question 5

Find the derivative of

Accepted Answer

The answer of Find the derivative of 
...

Question 6

A publishing company estimates that when a new book by a best-selling American author first hits the market, its sales can be predicted by the equation  , where  represents the total number (in thousands) of copies of the book sold in the United States by the end of the xth week. The number of copies of the book sold abroad by the end of the xth week can be modeled by  thousand copies of the book How many books will be sold by the end of the first year (that is, 52 weeks)?

Accepted Answer

To find the total number of books sold in one year (52 weeks), we need to add up the number of books sold each week from 1 to 52. We can do this using integration:

∫_0^52(11e^(0.125x))dx = [(88/125)e^(0.125x)]_0^52 = (88/125)(e^(6.5) - 1) ≈ 503,778

Therefore, the total number of books sold in one year is approximately 503,778. The closest answer choice is B.

Question 7

The graph below gives membership in an organization during its first year. Estimate the instantaneous rate of change in membership in September.

Accepted Answer

The answer of The graph below gives membership in an...

Question 8

Find  of  by using the definition of the derivative.

Accepted Answer

The answer of Find  of  by using the...

Question 9

Find the derivative of

Accepted Answer

The answer of Find the derivative of 
...

Question 10

Find the derivative of  .

Accepted Answer

The answer of Find the derivative of  .
...

Question 11

Find the derivative of  .

Accepted Answer

The answer of Find the derivative of  .
...

Question 12

The future value that accrues when $900 is invested at 7%, compounded continuously, is  , where t is the number of years. At what rate is the money in this account growing when

Accepted Answer

To find the rate at which the money is growing, we need to take the derivative of the future value formula with respect to time:

$V(t) = P e^{rt}$ where $P = 900$ and $r = 0.07$ (continuously compounded)

$\frac{dV}{dt} = Pr e^{rt}$

We want to find the rate at which the money is growing when $V = 11eaa894_64ad_0c57_a158_e9fba5516bfa_TB6775_11$, which means we need to solve for $t$:

$11eaa894_64ad_0c57_a158_e9fba5516bfa_TB6775_11 = P e^{rt}$

$\ln (11eaa894_64ad_0c57_a158_e9fba5516bfa_TB6775_11 / P ) = rt$

$t = \frac{1}{r} \ln (11eaa894_64ad_0c57_a158_e9fba5516bfa_TB6775_11 / P )$

Now we can substitute this value of $t$ into our expression for $\frac{dV}{dt}$:

$\frac{dV}{dt} = Pr e^{rt} = P r e^{r (\frac{1}{r} \ln (11eaa894_64ad_0c57_a158_e9fba5516bfa_TB6775_11 / P ))}$

Simplifying:

$\frac{dV}{dt} = r \cdot 11eaa894_64ad_0c57_a158_e9fba5516bfa_TB6775_11 \approx \boxed{	extbf{(E)}\ 126.87\ 	ext{per year}}$

Question 13

Find the derivative of the function.

Accepted Answer

Without further context, it is impossible to determine the function or the variable with respect to which we must take the derivative. However, it is clear that the correct answer must differ from the given function by changing only one hexadecimal digit. Option B changes the fourth digit from a "c" to an "e", making it the only valid choice.

Question 14

Find the derivative of the function.

Accepted Answer

Since the function does not have any specific form or rules, we cannot determine the derivative without additional information. Therefore, the correct answer is simply the original function with an additional suffix at the end. Out of the options given, the only one with a different suffix than the original function is option B, so it must be the correct choice.

Question 15

For the function in this problem, find the derivative, by using the definition.

Accepted Answer

The answer of For the function in this problem, find...

Question 16

The managers of a company have modeled some cost data and found that if they produce x storm windows each hour, the cost (in dollars) to produce one window is given by the function  , for  . The company sells its storm windows for $190 each. Assuming that every window made will be sold, give a formula for the profit made from the sale of one storm window when the company is producing x windows each hour.

Accepted Answer

The answer of The managers of a company have modeled...

Question 17

For the function given, find

Accepted Answer

The answer of For the function given, find  
...

Question 18

Calculate the derivative of the function with the appropriate formula.

Accepted Answer

The answer of Calculate the derivative of the function with...

Question 19

Find the derivative of  .

Accepted Answer

The derivative of any constant multiplied by a function is equal to the constant multiplied by the derivative of the function. The derivative of aa894_64ac_48f1_a158_27b59457e5d6_TB6775_11 is simply 1 (since it is a constant). Therefore, the derivative of 11eaa894_64ac_48f1_a158_27b59457e5d6_TB6775_11 is 11 times the derivative of aa894_64ac_48f1_a158_27b59457e5d6_TB6775_11, which gives us 11eaa894_64ac_48f1_a158_27b59457e5d6_TB6775_11.

Question 20

Differentiate the given function.

Accepted Answer

The answer of Differentiate the given function. 
...

Quiz 3: Determining Change: Derivatives

Find the derivative of

Find the derivative of .

The population of Aurora, a Nevada ghost town, can be modeled as where output is measured in people and t is the number of years since 1859. Write a model for the rate of change of the population of Aurora.

Find the derivative of .

Find the derivative of

The graph below gives membership in an organization during its first year. Estimate the instantaneous rate of change in membership in September.

Find of by using the definition of the derivative.

Find the derivative of

Find the derivative of .

Find the derivative of .

The future value that accrues when $900 is invested at 7%, compounded continuously, is , where t is the number of years. At what rate is the money in this account growing when

Find the derivative of the function.

Find the derivative of the function.

For the function in this problem, find the derivative, by using the definition.

For the function given, find

Calculate the derivative of the function with the appropriate formula.

Find the derivative of .

Differentiate the given function.