Question 1

Let  . Use logarithmic differentiation to calculate  .

Accepted Answer

The answer of Let  . Use logarithmic differentiation to...

Question 2

The derivative of  is
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The derivative of  is
A) 
B) 
C)...

Question 3

The population in a certain country was 10,900,000 in 1990 and 17,100,000 in 2005. The doubling time of the population is:
A) 52.7 years
B) 53.6 years
C) 31.3 years
D) 23.1 years
E) none of the above

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The answer of The population in a certain country was...

Question 4

Find an equation of the tangent line to the graph of the function  for  .

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The answer of Find an equation of the tangent line...

Question 5

Let  . Calculate  .

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The answer of Let  . Calculate  ....

Question 6

Evaluate the integrals:
A)  
B)

Accepted Answer

The answer of Evaluate the integrals:
A)  
B) ...

Question 7

The population of a country was  in 1980, whereas in 1990 it was  
A) Find the population in  
B) Determine the population's doubling time.
Assume that the rate of growth is proportional to the population.

Accepted Answer

The answer of The population of a country was ...

Question 8

Find the slope of the tangent line to the graph of the function  at  To find  , use the equality  or use a calculator.

Accepted Answer

The answer of Find the slope of the tangent line...

Question 9

The rate of change of the following function is proportional to  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The rate of change of the following...

Question 10

Evaluate the integrals using the given substitutions:
A)  
B)

Accepted Answer

The answer of Evaluate the integrals using the given substitutions:
A)...

Question 11

Consider the Gompertz differential equation  .
Define the function  by  . The differential equation for  is,
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Consider the Gompertz differential equation  .
Define...

Question 12

Evaluate the definite integrals:
A)  
B)  
C)

Accepted Answer

The answer of Evaluate the definite integrals:
A)  
B) ...

Question 13

Let  . Use logarithmic differentiation to calculate  .

Accepted Answer

The answer of Let  . Use logarithmic differentiation to...

Question 14

A population is modeled by a function  . Initially, the population counts 1000. The rate of change of the population is proportional to  . Find the population at time  years given that the doubling time is 8 years.

Accepted Answer

The answer of A population is modeled by a function...

Question 15

The population of a country was  in  and  in  . The population doubling time is:
A) 25 years 
B) 30.1 years 
C) 39.5 years 
D) 40.1 years 
E) none of the above

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The answer of The population of a country was ...

Question 16

Find  if  .

Accepted Answer

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Question 17

Compute the derivatives of the following functions:
A)  
B)  
C)

Accepted Answer

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A)...

Question 18

Find all solutions to  satisfying  .

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Question 19

Let  . Calculate  .

Accepted Answer

The answer of Let  . Calculate  ....

Question 20

Evaluate the integrals:
A)  
B)  
C)

Accepted Answer

The answer of Evaluate the integrals:
A)  
B)  
C)...

Quiz 7: Exponential Functions

Let . Use logarithmic differentiation to calculate .

The derivative of is

The population in a certain country was 10,900,000 in 1990 and 17,100,000 in 2005. The doubling time of the population is:

Find an equation of the tangent line to the graph of the function for .

Let . Calculate .

Evaluate the integrals: A) B)

The population of a country was in 1980, whereas in 1990 it was A) Find the population in B) Determine the population's doubling time. Assume that the rate of growth is proportional to the population.

Find the slope of the tangent line to the graph of the function at To find , use the equality or use a calculator.

The rate of change of the following function is proportional to .

Evaluate the integrals using the given substitutions: A) B)

Consider the Gompertz differential equation . Define the function by . The differential equation for is,

Evaluate the definite integrals: A) B) C)

Let . Use logarithmic differentiation to calculate .

A population is modeled by a function . Initially, the population counts 1000. The rate of change of the population is proportional to . Find the population at time years given that the doubling time is 8 years.

The population of a country was in and in . The population doubling time is:

Find if .

Compute the derivatives of the following functions: A) B) C)

Find all solutions to satisfying .

Let . Calculate .

Evaluate the integrals: A) B) C)