Question 1

Find the exponential function that satisfies the given conditions.
-Initial mass $= 29 \mathrm {~g}$, decreasing at a rate of $3.5 \%$ per day

Accepted Answer

A)  $m ( t ) = 29 \cdot 0.965 ^ { t }$ 
B)  $\mathrm { m } ( \mathrm { t } ) = 29 \cdot 1.35 ^ { \mathrm { t } }$ 
C)  $m ( t ) = 3.5 \cdot 0.71 ^ { t }$ 
D)  $m ( t ) = 29 \cdot 1.035 ^ { t }$ 
A)  $m ( t ) = 29 \cdot 0.965 ^ { t }$ 
B)  $\mathrm { m } ( \mathrm { t } ) = 29 \cdot 1.35 ^ { \mathrm { t } }$ 
C)  $m ( t ) = 3.5 \cdot 0.71 ^ { t }$ 
D)  $m ( t ) = 29 \cdot 1.035 ^ { t }$

Question 2

Determine a formula for the exponential function.
-The graph of an exponential function is given. Which of the following is the correct equation of the function?

Accepted Answer

A)  $y = 0.26 x$ 
B)  $y = 0.74 ^ { x }$ 
C)  $\mathrm { y } = 1.9 \mathrm { x }$ 
D)  $y = 3.6 ^ { x }$ 
A)  $y = 0.26 x$ 
B)  $y = 0.74 ^ { x }$ 
C)  $\mathrm { y } = 1.9 \mathrm { x }$ 
D)  $y = 3.6 ^ { x }$

Question 3

Evaluate the logarithm.
-$\ln \mathrm { e } ^ { 5 }$

Accepted Answer

A)  $\mathrm { e } ^ { 5 }$ 
B)  $5 \ln \mathrm { e }$ 
C)  1 
D)  5 
A)  $\mathrm { e } ^ { 5 }$ 
B)  $5 \ln \mathrm { e }$ 
C)  1 
D)  5

Question 4

Choose the graph which matches the function.
-$$f ( x ) = 3 ^ { x - 1 }$$

Accepted Answer

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

Question 5

Find the amount accumulated after investing a principal P for t years at an interest rate r.
-P = $4511, t = 5 , r = 7.3% , compounded quarterly (k = 4)

Accepted Answer

A)  $6456.04 
B)  $6416.10 
C)  $6476.81 
D)  $6490.98 
A)  $6456.04 
B)  $6416.10 
C)  $6476.81 
D)  $6490.98

Question 6

Find the amount accumulated after investing a principal P for t years at an interest rate r.
-P = $1,000, t = 2, r = 6% , compounded annually (k = 1)

Accepted Answer

A)  $1191.02 
B)  $1060.00 
C)  $1123.60 
D)  $123.6 
A)  $1191.02 
B)  $1060.00 
C)  $1123.60 
D)  $123.6

Question 7

Solve the problem.
-How long will it take for $5100 to grow to $5300 at an interest rate of 4.4% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Accepted Answer

A)  0.87 yr 
B)  0.09 yr 
C)  87.42 yr 
D)  0.03 yr 
A)  0.87 yr 
B)  0.09 yr 
C)  87.42 yr 
D)  0.03 yr

Question 8

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry,
boundedness, extrema, asymptotes, and end behavior.
-f(x) = - log (x + 2)

Accepted Answer

@#IMG-DLM&
The domain is @#LAT-DLM&, and the range is all re

Question 9

Determine the doubling time of the investment.
-8% APR compounded continuously

Accepted Answer

A)  8.66 years 
B)  6.93 years 
C)  17.33 years 
D)  13 years 
A)  8.66 years 
B)  6.93 years 
C)  17.33 years 
D)  13 years

Question 10

Solve the equation.
-$\log x ^ { 2 } = 8$

Accepted Answer

A)  $10 ^ { 8 }$ 
B)  $673.977$ 
C)  $\pm 2.828$ 
D)  $\pm 10,000$ 
A)  $10 ^ { 8 }$ 
B)  $673.977$ 
C)  $\pm 2.828$ 
D)  $\pm 10,000$

Question 11

Use a calculator to find an approximate solution to the equation.
-$$\left( \frac { 1 } { 2 } \right) ^ { x } = 24$$

Accepted Answer

A)  $4.585$ 
B)  $- 12.000$ 
C)  $- 4.585$ 
D)  $- 0.218$ 
A)  $4.585$ 
B)  $- 12.000$ 
C)  $- 4.585$ 
D)  $- 0.218$

Question 12

Solve the inequality graphically.
-$\left( \frac { 1 } { 5 } \right) ^ { x } > \left( \frac { 1 } { 3 } \right) ^ { x }$

Accepted Answer

A) $x 0$ C) $x > 1$ D) $x < 0$ A) $x 0$ C) $x > 1$ D) $x < 0$

Question 13

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry,
boundedness, extrema, asymptotes, and end behavior.
-$$f ( x ) = \ln ( x + 3 )$$

Accepted Answer

@#IMG-DLM&
The domain is @#LAT-DLM&, and the range is all re

Question 14

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$f(x)=\ln (x-5) \text {; relative to } f(x)=\ln x$

Accepted Answer

A)  Moved left 5 units
  
B)  Moved right 5 units
  
C)  Moved left 5 units
  
D)  Moved right 5 units
  
A)  Moved left 5 units
  
B)  Moved right 5 units
  
C)  Moved left 5 units
  
D)  Moved right 5 units

Question 15

Determine the doubling time of the investment.
-8.25% APR compounded annually

Accepted Answer

A)  13.12 years 
B)  8.74 years 
C)  17.49 years 
D)  7 years 
A)  13.12 years 
B)  8.74 years 
C)  17.49 years 
D)  7 years

Question 16

Solve the problem.
-Use the data in the table to compute a logistic regression model for the population of the city t years after $1900 .$ Then use your model to predict the city's population in $1980 .$

Accepted Answer

A)  $4.2$ million 
B)  $4.7$ million 
C)  $4.5$ million 
D)  $3.9$ million 
A)  $4.2$ million 
B)  $4.7$ million 
C)  $4.5$ million 
D)  $3.9$ million

Question 17

Solve the problem.
-The population of a small country increases according to the function $\mathrm { B } = 900,000 \mathrm { e } ^ { 0.02 \mathrm { t } }$, where $\mathrm { t }$ is measured in years. How many people will the country have after 4 years?

Accepted Answer

A)  $1,082,038$ 
B)  $987.219$ 
C)  $2,273,156$ 
D)  974,958 
A)  $1,082,038$ 
B)  $987.219$ 
C)  $2,273,156$ 
D)  974,958

Question 18

Solve the problem.
-By how many orders of magnitude do two earthquakes differ if one is rated 2.7 on the Richter scale and the other is rated 5.1?

Accepted Answer

A)  1.9 
B)  4.8 
C)  1.2 
D)  2.4 
A)  1.9 
B)  4.8 
C)  1.2 
D)  2.4

Question 19

Solve the equation by changing it to exponential form.
-$$\log x = 2$$

Accepted Answer

A)  $x = 210$ 
B)  $x = 20$ 
C)  $x = - 20$ 
D)  $x = 10 ^ { 2 }$ 
A)  $x = 210$ 
B)  $x = 20$ 
C)  $x = - 20$ 
D)  $x = 10 ^ { 2 }$

Question 20

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry,
boundedness, extrema, asymptotes, and end behavior.
-f(x) = log (x - 4)

Accepted Answer

The domain is @#LAT-DLM&, and the range is all rea

Find the exponential function that satisfies the given conditions. -Initial mass $= 29 \mathrm {~g}$ , decreasing at a rate of $3.5 \%$ per day

Determine a formula for the exponential function. -The graph of an exponential function is given. Which of the following is the correct equation of the function?

Evaluate the logarithm. - $\ln \mathrm { e } ^ { 5 }$

Choose the graph which matches the function. - $f ( x ) = 3 ^ { x - 1 }$ $Choose the graph which matches the function. - f ( x ) = 3 ^ { x - 1 }$

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $4511, t = 5 , r = 7.3% , compounded quarterly (k = 4)

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $1,000, t = 2, r = 6% , compounded annually (k = 1)

Solve the problem. -How long will it take for $5100 to grow to $5300 at an interest rate of 4.4% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. -f(x) = - log (x + 2)

Determine the doubling time of the investment. -8% APR compounded continuously

Solve the equation. - $\log x ^ { 2 } = 8$

Use a calculator to find an approximate solution to the equation. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 24$

Solve the inequality graphically. - $\left( \frac { 1 } { 5 } \right) ^ { x } > \left( \frac { 1 } { 3 } \right) ^ { x }$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = \ln ( x + 3 )$

Graph the function. Describe its position relative to the graph of the indicated basic function. - $f(x)=\ln (x-5) \text {; relative to } f(x)=\ln x$ $Graph the function. Describe its position relative to the graph of the indicated basic function. - f(x)=\ln (x-5) \text {; relative to } f(x)=\ln x$

Determine the doubling time of the investment. -8.25% APR compounded annually

Solve the problem. -Use the data in the table to compute a logistic regression model for the population of the city t years after $1900 .$ Then use your model to predict the city's population in $1980 .$

Solve the problem. -The population of a small country increases according to the function $\mathrm { B } = 900,000 \mathrm { e } ^ { 0.02 \mathrm { t } }$ , where $\mathrm { t }$ is measured in years. How many people will the country have after 4 years?

Solve the problem. -By how many orders of magnitude do two earthquakes differ if one is rated 2.7 on the Richter scale and the other is rated 5.1?

Solve the equation by changing it to exponential form. - $\log x = 2$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. -f(x) = log (x - 4)

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Polynomial, Power, and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

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Analytic Geometry in Two and Three Dimensions

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An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 3: Exponential, Logistic, and Logarithmic Functions

Find the exponential function that satisfies the given conditions. -Initial mass =29 g= 29 \mathrm {~g}=29 g , decreasing at a rate of 3.5%3.5 \%3.5% per day