Question 1

Match the function with its graph.
-f(x) = log x + log(x - 2)

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 2

Write the expression using only the indicated logarithms.
-$\log 4 x$ using common logarithms

Accepted Answer

A)  $\frac { \log 4 } { \log x }$ 
B)  $\log x \cdot \log 4$ 
C)  $\log x + \log 4$ 
D)  $\frac { \log x } { \log 4 }$

Question 3

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of
logarithms or multiples of logarithms.
-log8 (xy)

Accepted Answer

A)  log4 x + log4 y 
B)  log8 x - log8 y 
C)  log4 x - log4 y 
D)  log8 x + log8 y

Question 4

Find the amount accumulated after investing a principal P for t years at an interest rate r.
-P = $12,000, t = 3, r = 10%, compounded quarterly (k = 4)

Accepted Answer

A)  $15,972.00 
B)  $15,745.04 
C)  $4138.67 
D)  $16,138.67

Question 5

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$f(x)=-3^{x+3} \text {; relative to } f(x)=3^{x}$

Accepted Answer

A)  Moved right 3 unit(s);
reflected across $x$-axis
 
B)  Moved right 3 unit(s);
 reflected across $\mathrm { x }$-axis
 
C)  Moved left 3 unit(s);
reflected across $\mathrm { x }$-axis 
 
D)  Moved left 3 unit(s);
reflected across $x$-axis

Question 6

Solve the problem.
-Find the present value of a loan with an annual interest rate of 6.7% and periodic payments of $288.46 for a term of 3 years, with payments made and interest charged 12 times per year.

Accepted Answer

A)  $18,767.66 
B)  $7507.06 
C)  $16,890.89 
D)  $9383.83

Question 7

Choose the graph which matches the function.
-$$f ( x ) = 4 e ^ { - x }$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 8

Determine a formula for the exponential function.
-

Accepted Answer

A)  $f ( x ) = 36 \cdot 2 ^ { x }$ 
B)  $f ( x ) = 9 \cdot 2 ^ { x - 2 }$ 
C)  $f ( x ) = 9 \cdot \left( \frac { 1 } { 2 } \right) ^ { x }$ 
D)  $f ( x ) = 9 \cdot 2 ^ { - x } + 2$

Question 9

Solve the problem.
-The number of bacteria growing in an incubation culture increases with time according to $B = 4300 ( 4 ) ^ { x }$, where $x$ is time in days. Find the number of bacteria when $x = 0$ and $x = 5$.

Accepted Answer

A)  $4300,86,000$ 
B)  $4300,4,403,200$ 
C)  $17,200,4,403,200$ 
D)  $4300,1,100,800$

Question 10

Solve the problem.
-Find a natural logarithmic regression equation for the following data and use it estimate the production level for the year 1980. (For the regression equation, assume $t = 0$ is the year 1950.)

Accepted Answer

A)  $58.05$ million 
B)  $271.893333$ million 
C)  $60.65$ million 
D)  $69.4291429$ million

Question 11

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$$f ( x ) = e ^ { 2 x } + 4 ; \text { relative to } f ( x ) = e ^ { x }$$

Accepted Answer

A)  Shrunk horizontally;
moved up 4 unit(s)
 
B)  Stretched horizontally;
moved down 4 unit(s)
 
C)  Shrunk horizontally;
moved down 4 unit(s)
 
D)  Stretched horizontally;
 moved up 4 unit(s)

Question 12

Solve the problem.
-If x is the hydrogen ion concentration of a sample of water, then the pH of that water sample is f(x) = -log x. If the pH of the water from one lake is 4.6 and the pH of the water from a second lake is 5.4, how many times
Greater is the hydrogen ion concentration of the second lake than the hydrogen ion concentration of the first
Lake? Round your answer to the nearest hundredth.

Accepted Answer

A)  6.31 
B)  0.16 
C)  14.92 
D)  7.11

Question 13

Evaluate the logarithm.
-$\log _ { 8 } \sqrt [ 4 ] { \frac { 1 } { 64 } }$

Accepted Answer

A)  $- 2$ 
B)  $- \frac { 1 } { 2 }$ 
C)  2 
D)  $\frac { 1 } { 2 }$

Question 14

Solve the problem.
-In September 1998 the population of the country of West Goma in millions was modeled by $f ( x ) = 17.8 e ^ { 0.0018 x }$. At the same time the population of East Goma in millions was modeled by $g ( x ) = 13.1 e ^ { 0.0148 x }$. In both formulas $x$ is the year, where $x = 0$ corresponds to September 1998. Assuming these trends continue, estimate what the population will be when the populations are equal.

Accepted Answer

A)  1 million 
B)  17 million 
C)  19 million 
D)  18 million

Question 15

Compute the exact value of the function for the given x-value without using a calculator.
-$f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$ for $x = - 3$

Accepted Answer

A)  $\frac { 1 } { 64 }$ 
B)  64 
C)  $- 12$ 
D)  $- \frac { 1 } { 64 }$

Question 16

Solve the problem.
-Suppose you contribute $50 per month into a fund that earns 6.34% annual interest. What is the value of your investment after 29 years?

Accepted Answer

A)  $49,754.30 
B)  $89,557.73 
C)  $64,680.59 
D)  $39,803.44

Question 17

Use the change of base rule to find the logarithm to four decimal places.
-$\log _ { 5 } 3$

Accepted Answer

A)  $1.3652$ 
B)  $0.6826$ 
C)  $1.4650$ 
D)  $- 0.6826$

Question 18

Find the following using a calculator. Round to four decimal places.
-$\ln 0.981$

Accepted Answer

A)  $- 0.0192$ 
B)  $0.0083$ 
C)  $- 0.0083$ 
D)  $0.0192$

Question 19

Decide whether the function is an exponential growth or exponential decay function and find the constant percentage
rate of growth or decay.
-$$f ( x ) = 20,092 \cdot 0.867 ^ { x }$$

Accepted Answer

A)  Exponential decay function; $0.133 \%$ 
B)  Exponential decay function; $- 13.3 \%$ 
C)  Exponential growth function; $0.133 \%$ 
D)  Exponential grow th function; $- 13.3 \%$

Question 20

Solve the problem.
-The population of wolves in a state park after t years is modeled by the function $\mathrm { P } ( \mathrm { t } ) = \frac { 1200 } { 1 + 99 \mathrm { e } ^ { - 0.3 \mathrm { t } } }$. What was the initial population of wolves?

Accepted Answer

A)  12 
B)  99 
C)  1200 
D)  24

Exam 3: Exponential, Logistic, and Logarithmic Functions

Match the function with its graph. -f(x) = log x + log(x - 2)

Write the expression using only the indicated logarithms. - $\log 4 x$ using common logarithms

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. -log8 (xy)

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $12,000, t = 3, r = 10%, compounded quarterly (k = 4)

Solve the problem. -Find the present value of a loan with an annual interest rate of 6.7% and periodic payments of $288.46 for a term of 3 years, with payments made and interest charged 12 times per year.

Choose the graph which matches the function. - $f ( x ) = 4 e ^ { - x }$ $Choose the graph which matches the function. - f ( x ) = 4 e ^ { - x } A) B) C) D)$

Determine a formula for the exponential function. - $Determine a formula for the exponential function. - A) f ( x ) = 36 \cdot 2 ^ { x } B) f ( x ) = 9 \cdot 2 ^ { x - 2 } C) f ( x ) = 9 \cdot \left( \frac { 1 } { 2 } \right) ^ { x } D) f ( x ) = 9 \cdot 2 ^ { - x } + 2$

Solve the problem. -The number of bacteria growing in an incubation culture increases with time according to $B = 4300 ( 4 ) ^ { x }$ , where $x$ is time in days. Find the number of bacteria when $x = 0$ and $x = 5$ .

Solve the problem. -Find a natural logarithmic regression equation for the following data and use it estimate the production level for the year 1980. (For the regression equation, assume $t = 0$ is the year 1950.)

Evaluate the logarithm. - $\log _ { 8 } \sqrt [ 4 ] { \frac { 1 } { 64 } }$

Compute the exact value of the function for the given x-value without using a calculator. - $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$ for $x = - 3$

Solve the problem. -Suppose you contribute $50 per month into a fund that earns 6.34% annual interest. What is the value of your investment after 29 years?

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 5 } 3$

Find the following using a calculator. Round to four decimal places. - $\ln 0.981$

Decide whether the function is an exponential growth or exponential decay function and find the constant percentage rate of growth or decay. - $f ( x ) = 20,092 \cdot 0.867 ^ { x }$

Solve the problem. -The population of wolves in a state park after t years is modeled by the function $\mathrm { P } ( \mathrm { t } ) = \frac { 1200 } { 1 + 99 \mathrm { e } ^ { - 0.3 \mathrm { t } } }$ . What was the initial population of wolves?

Exam 3: Exponential, Logistic, and Logarithmic Functions

Match the function with its graph. -f(x) = log x + log(x - 2)

Write the expression using only the indicated logarithms. - log⁡4x\log 4 xlog4x using common logarithms

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. -log8 (xy)

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $12,000, t = 3, r = 10%, compounded quarterly (k = 4)

Graph the function. Describe its position relative to the graph of the indicated basic function. - f(x) =−3x+3; relative to f(x) =3xf(x) =-3^{x+3} \text {; relative to } f(x) =3^{x}f(x) =−3x+3; relative to f(x) =3x

Solve the problem. -Find the present value of a loan with an annual interest rate of 6.7% and periodic payments of $288.46 for a term of 3 years, with payments made and interest charged 12 times per year.

Choose the graph which matches the function. - f(x) =4e−xf ( x ) = 4 e ^ { - x }f(x) =4e−x

Determine a formula for the exponential function. -

Solve the problem. -The number of bacteria growing in an incubation culture increases with time according to B=4300(4) xB = 4300 ( 4 ) ^ { x }B=4300(4) x , where xxx is time in days. Find the number of bacteria when x=0x = 0x=0 and x=5x = 5x=5 .

Solve the problem. -Find a natural logarithmic regression equation for the following data and use it estimate the production level for the year 1980. (For the regression equation, assume t=0t = 0t=0 is the year 1950.)

Graph the function. Describe its position relative to the graph of the indicated basic function. - f(x) =e2x+4; relative to f(x) =exf ( x ) = e ^ { 2 x } + 4 ; \text { relative to } f ( x ) = e ^ { x }f(x) =e2x+4; relative to f(x) =ex

Evaluate the logarithm. - log⁡81644\log _ { 8 } \sqrt [ 4 ] { \frac { 1 } { 64 } }log8​4641​​

Compute the exact value of the function for the given x-value without using a calculator. - f(x) =(14) xf ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }f(x) =(41​) x for x=−3x = - 3x=−3