Question 1

Find the derivative of the function   .

Accepted Answer

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

Question 2

Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places:The rate of change of y is proportional to y. When x = 0, y = 4 and when x = 1, y = 16. What is the value of y when x = 7?

Accepted Answer

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

Question 3

The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours there are 140 bacteria in the culture and after 4 hours there are 370 bacteria in the culture. Answer the following questions, rounding numerical answers to four decimal places.(i) Find the initial population.(ii) Write an exponential growth model for the bacteria population. Let t represent time in hours.(iii) Use the model to determine the number of bacteria after 8 hours.(iv) After how many hours will the bacteria count be 25,000?

Accepted Answer

A) (i) 52.9730 ; (ii)   ; (iii) 2,584.3367 ; (iv) 12.6702 hr 
B) (i) 55.1230 ; (ii)   ; (iii) 5,271.7880 ; (iv) 17.2327 hr 
C) (i) 58.7530 ; (ii)   ; (iii) 8,023.2414 ; (iv) 19.3439 hr 
D) (i) 60.3130 ; (ii)   ; (iii) 10,675.7049 ; (iv) 21.1233 hr 
E) (i) 52.9730 ; (ii)   ; (iii) 3,897.0708 ; (iv) 15.0047 hr 
A) (i) 52.9730 ; (ii)   ; (iii) 2,584.3367 ; (iv) 12.6702 hr 
B) (i) 55.1230 ; (ii)   ; (iii) 5,271.7880 ; (iv) 17.2327 hr 
C) (i) 58.7530 ; (ii)   ; (iii) 8,023.2414 ; (iv) 19.3439 hr 
D) (i) 60.3130 ; (ii)   ; (iii) 10,675.7049 ; (iv) 21.1233 hr 
E) (i) 52.9730 ; (ii)   ; (iii) 3,897.0708 ; (iv) 15.0047 hr

Question 4

The isotope   has a half-life of 5,715 years. After 20,000 years, a sample of the isotope is reduced 0.1 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 2,000 years? Round your answers to four decimal places.

Accepted Answer

A) 0.6786, 0.5324 
B) 0.5655, 0.4437 
C) 0.9048, 0.7099 
D) 1.4703, 1.1536 
E) 1.1310, 0.8874 
A) 0.6786, 0.5324 
B) 0.5655, 0.4437 
C) 0.9048, 0.7099 
D) 1.4703, 1.1536 
E) 1.1310, 0.8874

Question 5

Find   .

Accepted Answer

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

Question 6

Use implicit differentiation to find   .

Accepted Answer

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

Question 7

Suppose that the population (in millions) of Egypt in 2007 was 80.3 and that the expected continuous annual rate of change of the population is 0.017. Find the exponential growth model   for the population by letting   correspond to 2000. Round your answer to four decimal places.

Accepted Answer

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

Question 8

Find   .

Accepted Answer

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

Question 9

The value V (in dollars) of an item t years after it is purchased is   . Find the rate of change of V with respect to t when   . Round your answer to two decimal places.

Accepted Answer

A) -1839.21 dollars/year 
B) 245.40 dollars/year 
C) -1324.10 dollars/year 
D) 1839.21 dollars/year 
E) -245.40 dollars/year 
A) -1839.21 dollars/year 
B) 245.40 dollars/year 
C) -1324.10 dollars/year 
D) 1839.21 dollars/year 
E) -245.40 dollars/year

Question 10

Find the indefinite integral   .

Accepted Answer

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

Question 11

Locate any relative extrema and inflection points of the function   . Use a graphing utility to confirm your results.

Accepted Answer

A) relative maximum value:   ; inflection point: (0, 0) 
B) relative minimum value:   ; inflection point: (0, 0) 
C) relative minimum value:   ; no inflection points 
D) relative minimum value:   ; no inflection points 
E) relative maximum value:   ; no inflection points 
A) relative maximum value:   ; inflection point: (0, 0) 
B) relative minimum value:   ; inflection point: (0, 0) 
C) relative minimum value:   ; no inflection points 
D) relative minimum value:   ; no inflection points 
E) relative maximum value:   ; no inflection points

Question 12

Find the derivative of the function   .

Accepted Answer

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

Question 13

Solve the differential equation.

Accepted Answer

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

Question 14

Suppose the demand equation for a product is   Find the average price p on the interval   . Round your answer to the nearest dollar.

Accepted Answer

A) $67 
B) $74 
C) $86 
D) $106 
E) $732 
A) $67 
B) $74 
C) $86 
D) $106 
E) $732

Find the derivative of the function .

The isotope has a half-life of 5,715 years. After 20,000 years, a sample of the isotope is reduced 0.1 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 2,000 years? Round your answers to four decimal places.

Find .

Use implicit differentiation to find .

Suppose that the population (in millions) of Egypt in 2007 was 80.3 and that the expected continuous annual rate of change of the population is 0.017. Find the exponential growth model for the population by letting correspond to 2000. Round your answer to four decimal places.

Find .

The value V (in dollars) of an item t years after it is purchased is . Find the rate of change of V with respect to t when . Round your answer to two decimal places.

Find the indefinite integral .

Locate any relative extrema and inflection points of the function . Use a graphing utility to confirm your results.

Find the derivative of the function .

Solve the differential equation.

Suppose the demand equation for a product is Find the average price p on the interval . Round your answer to the nearest dollar.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Exam 9: Exponential and Logarithmic Functions and Calculus

Find the derivative of the function .

The isotope has a half-life of 5,715 years. After 20,000 years, a sample of the isotope is reduced 0.1 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 2,000 years? Round your answers to four decimal places.

Find .

Use implicit differentiation to find .

Suppose that the population (in millions) of Egypt in 2007 was 80.3 and that the expected continuous annual rate of change of the population is 0.017. Find the exponential growth model for the population by letting correspond to 2000. Round your answer to four decimal places.

Find .

The value V (in dollars) of an item t years after it is purchased is . Find the rate of change of V with respect to t when . Round your answer to two decimal places.

Find the indefinite integral .

Locate any relative extrema and inflection points of the function . Use a graphing utility to confirm your results.

Find the derivative of the function .

Solve the differential equation.

Suppose the demand equation for a product is Find the average price p on the interval . Round your answer to the nearest dollar.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters