Question 1

Find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Use the definition of a logarithm to prove   .Hint: Let   and   .Then,   and   .

Accepted Answer

A) Let   and
  so that
  and
  .Then
  and by definition,
  ; that is
  . 
B) Let   and
  so that
  and
  .Then
  and by definition,
  ; that is
  . 
C) Let   and
  so that
  and
  .Then
  and by definition,
  ; that is
  . 
A) Let   and
  so that
  and
  .Then
  and by definition,
  ; that is
  . 
B) Let   and
  so that
  and
  .Then
  and by definition,
  ; that is
  . 
C) Let   and
  so that
  and
  .Then
  and by definition,
  ; that is
  .

Question 3

Use logarithms to solve the equation for t.Round your answer to four decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by   .
What is the price of the commodity at   ?
$   /unit
How fast is the price of the commodity changing at   ?   (increasing / decreasing) at the rate of $   /wk
Find the equilibrium price of the commodity.(Hint: It's given by   .Also, use the fact that   .)
$   /unit

Accepted Answer

The answer of The price of a certain commodity in...

Question 5

Find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Given that a quantity Q(t) is described by the exponential growth function   where t is measured in minutes.What is the growth constant? What quantity is present initially? Complete the table of values.Round your answers to the nearest integer.

Accepted Answer

A) k = 600; Q = 0.03 t 0 10 20 100
Q 600 815 1,104 12,051 
B) k = 0.03; Q = 600 t 0 10 20 100
Q 600 810 1,104 12,162 
C) k = 0.03; Q = 600 t 0 10 20 100
Q 600 810 1,093 12,051 
D) k = 600; Q = 0.03 t 0 10 20 100
Q 600 810 1,093 12,051 
A) k = 600; Q = 0.03 t 0 10 20 100
Q 600 815 1,104 12,051 
B) k = 0.03; Q = 600 t 0 10 20 100
Q 600 810 1,104 12,162 
C) k = 0.03; Q = 600 t 0 10 20 100
Q 600 810 1,093 12,051 
D) k = 600; Q = 0.03 t 0 10 20 100
Q 600 810 1,093 12,051

Question 7

Use logarithmic differentiation to find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Determine whether the statement is true or false.If it is true, explain why it is true.If it is false, give an example to show why it is false.
The function   is continuous for all   .

Accepted Answer

The function @#IMG-DLM& is continuous an

Question 9

Find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

Bernie invested a sum of money 7 year(s) ago in a savings account, which has since paid interest at the rate of 8% / year compounded quarterly.His investment is now worth $22,608.44.How much did he originally invest?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Use logarithms to solve the equation for t.Round your answer to four decimal places.   t = __________

Accepted Answer

The answer of Use logarithms to solve the equation for...

Question 12

Sketch the graph of the equation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

The Estradas are planning to buy a house 4 year(s) from now.Housing experts in their area have estimated that the cost of a home will increase at a rate of 8% / year during that 4-year period.If this economic prediction holds true, how much can they expect to pay for a house that currently costs $40,000? Round your answer to two decimal places.

Accepted Answer

A) $54,742.76 
B) $54,419.56 
C) $55,026.64 
D) $55,085.11 
A) $54,742.76 
B) $54,419.56 
C) $55,026.64 
D) $55,085.11

Question 14

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 15

A condominium complex was purchased by a group of private investors for $1.5 million and sold 7 year(s) later for $3.7 million.Find the annual rate of return (compounded continuously) on their investment.Round your answer to the nearest hundredth.
Annual rate is __________% per year.

Accepted Answer

The answer of A condominium complex was purchased by a...

Question 16

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 17

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by   . How fast is the price of the commodity changing at   ?

Accepted Answer

A) Increasing at the rate of $19/wk. 
B) Decreasing at the rate of $19/wk. 
C) Increasing at the rate of $14/wk. 
D) Decreasing at the rate of $14/wk. 
E) Increasing at the rate of $5/wk. 
A) Increasing at the rate of $19/wk. 
B) Decreasing at the rate of $19/wk. 
C) Increasing at the rate of $14/wk. 
D) Decreasing at the rate of $14/wk. 
E) Increasing at the rate of $5/wk.

Question 18

Solve the equation for x.

Accepted Answer

The answer of Solve the equation for x.  ...

Question 19

For children between the ages of 5 and 13 years old, the Ehrenberg equation   gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child.Use differentials to estimate the change in the weight of a child who grows from 0.8 m to 1 m.Round the answer to the nearest tenth.
__________ kg

Accepted Answer

The answer of For children between the ages of 5...

Question 20

Having received a large inheritance, a child's parents wish to establish a trust for the child's college education.If 7 year(s) from now they need an estimated $90,000, how much should they set aside in trust now, if they invest the money at the given rate of interest.Round your answer to the nearest cent.
15.5 compounded quarterly
$__________
15.5 compounded continuously
$__________

Accepted Answer

The answer of Having received a large inheritance, a child's...

Find the derivative of the function.

Use the definition of a logarithm to prove .Hint: Let and .Then, and .

Use logarithms to solve the equation for t.Round your answer to four decimal places.

Find the derivative of the function.

Given that a quantity Q(t) is described by the exponential growth function where t is measured in minutes.What is the growth constant? What quantity is present initially? Complete the table of values.Round your answers to the nearest integer.

Use logarithmic differentiation to find the derivative of the function.

Determine whether the statement is true or false.If it is true, explain why it is true.If it is false, give an example to show why it is false. The function is continuous for all .

Find the derivative of the function.

Bernie invested a sum of money 7 year(s) ago in a savings account, which has since paid interest at the rate of 8% / year compounded quarterly.His investment is now worth $22,608.44.How much did he originally invest?

Use logarithms to solve the equation for t.Round your answer to four decimal places. t = __________

Sketch the graph of the equation.

Find the derivative of the function.

A condominium complex was purchased by a group of private investors for $1.5 million and sold 7 year(s) later for $3.7 million.Find the annual rate of return (compounded continuously) on their investment.Round your answer to the nearest hundredth. Annual rate is __________% per year.

Find the derivative of the function.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . How fast is the price of the commodity changing at ?

Solve the equation for x.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 5: Exponential and Logarithmic Functions

Find the derivative of the function.

Use the definition of a logarithm to prove .Hint: Let and .Then, and .

Use logarithms to solve the equation for t.Round your answer to four decimal places.

Find the derivative of the function.

Given that a quantity Q(t) is described by the exponential growth function where t is measured in minutes.What is the growth constant? What quantity is present initially? Complete the table of values.Round your answers to the nearest integer.

Use logarithmic differentiation to find the derivative of the function.

Determine whether the statement is true or false.If it is true, explain why it is true.If it is false, give an example to show why it is false. The function is continuous for all .

Find the derivative of the function.

Bernie invested a sum of money 7 year(s) ago in a savings account, which has since paid interest at the rate of 8% / year compounded quarterly.His investment is now worth $22,608.44.How much did he originally invest?

Use logarithms to solve the equation for t.Round your answer to four decimal places. t = __________

Sketch the graph of the equation.

Find the derivative of the function.

A condominium complex was purchased by a group of private investors for $1.5 million and sold 7 year(s) later for $3.7 million.Find the annual rate of return (compounded continuously) on their investment.Round your answer to the nearest hundredth. Annual rate is __________% per year.

Find the derivative of the function.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . How fast is the price of the commodity changing at ?

Solve the equation for x.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters