Question 1

Evaluate the logarithm.
-$\log 100,000$

Accepted Answer

A)  1 
B)  $- 5$ 
C)  10 
D)  5

Question 2

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
-$\log _ { 2 } 12 - \log _ { 2 } y$

Accepted Answer

A)  $\log _ { 2 } y / 12$ 
B)  $\log _ { 4 } 12 / y$ 
C)  $\log _ { 2 } 12 / \mathrm { y }$ 
D)  $\log _ { 2 } ( 12 - y )$

Question 3

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$$f ( x ) = 1 - 6 ^ { - x } ; \text { relative to } f ( x ) = 6 ^ { x }$$

Accepted Answer

A)  Reflected across y-axis;
reflected across x-axis;
moved up 1 unit(s)
 
B)  Moved up 1 unit(s);
reflected across, y-axis;
reflected across $x$-axis;
 
C)  Reflected across y-axis;
reflected across $x$-axis;
moved down 1 unit(s)
 
D)  Moved up 1 unit(s);
reflected across, y-axis;
reflected across $x$-axis;

Question 4

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( x - 2 ) + 5 ; \quad g ( x ) = \ln x$$

Accepted Answer

A)  Translate 2 units to the left and 5 units up. 
B)  Translate 5 units to the left and 2 units down. 
C)  Translate 2 units to the right and 5 units down. 
D)  Translate 2 units to the right and 5 units up.

Question 5

Match the function f with its graph.
-$$f ( x ) = \log _ { 5 } ( x - 1 )$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 6

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
-$$\frac { 1 } { 2 } \log _ { a } x + 3 \log _ { a } y - 2 \log _ { a } x$$

Accepted Answer

A)  $\log _ { a } x ^ { 2 } y ^ { 3 }$ 
B)  $\log _ { a } x ^ { 4 } y ^ { 3 }$ 
C)  $\log _ { a } \sqrt { x } y ^ { 3 }$ 
D)  $\log _ { a } \left( \frac { y ^ { 3 } } { x ^ { 3 / 2 } } \right)$

Question 7

Solve the problem.
-Find the future value accumulated in an annuity after investing periodic payments of $134 for 8 years at an annual interest rate of 5%, with payments made and credited 4 times per year.

Accepted Answer

A)  $3139.66 
B)  $6279.31 
C)  $9418.97 
D)  $5232.76

Question 8

Determine the function which corresponds to the given graph.
-
The asymptote is $x = - 2$.

Accepted Answer

A)  $y = \ln ( x - 2 )$ 
B)  $y = \ln x + 2$ 
C)  $y = \ln ( x + 2 )$ 
D)  $y = \ln x - 2$

Question 9

Solve the problem.
-Suppose you contribute to a fund that earns 5.5% annual interest. What should your quarterly payment be if you want to accumulate $190,000 in 18 years?

Accepted Answer

A)  $1873.72 
B)  $12,491.45 
C)  $1561.43 
D)  $2342.15

Question 10

Match the function f with its graph.
-$$f ( x ) = \log _ { 5 } ( - x )$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 11

Solve the problem.
-Find the present value of a loan with an annual interest rate of 5.9% and periodic payments of $778.63 for a term of 7 years, with payments made and interest charged 12 times per year.

Accepted Answer

A)  $96,254.83 
B)  $53,474.90 
C)  $42,779.92 
D)  $106,949.81

Question 12

Provide an appropriate response.
-The function $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. What is the annual interest rate?

Accepted Answer

The answer of Provide an appropriate response.
-The function \(f (...

Question 13

Find the domain of the function.
-$$f ( x ) = \log _ { 4 } \left( 100 - x ^ { 2 } \right)$$

Accepted Answer

A)  $[ - 10,10 ]$ 
B)  $( - 100,100 )$ 
C)  $( - 10,10 )$ 
D)  $( - \infty , - 10 ) \cup ( 10 , \infty )$

Question 14

Solve the equation.
-$\log ( 3 + x ) - \log ( x - 2 ) = \log 2$

Accepted Answer

A)  $- 7$ 
B)  $\frac { 1 } { 2 }$ 
C)  7 
D)  $\varnothing$

Question 15

Find the amount accumulated after investing a principal P for t years at an interest rate r.
-P = $1,000, t = 4, r = 4%, compounded semiannually (k = 2)

Accepted Answer

A)  $1148.69 
B)  $1169.86 
C)  $171.66 
D)  $1171.66

Question 16

Find the exponential function that satisfies the given conditions.
-Initial population $= 1013$, doubling every 6 hours

Accepted Answer

A)  $\mathrm { P } ( \mathrm { t } ) = 6 \cdot 2 ^ { \mathrm { t } }$ 
B)  $P ( t ) = 1013 \cdot 2 ^ { t / 6 }$ 
C)  $P ( t ) = 1013 \cdot \left( \frac { 1 } { 2 } \right) ^ { t / 6 }$ 
D)  $P ( t ) = 1013 \cdot 2 ^ { 6 t }$

Question 17

Determine the function which corresponds to the given graph.
-
The asymptote is $x = - 3$

Accepted Answer

A)  $y = \log ( 3 - x )$ 
B)  $y = - \log ( x - 3 )$ 
C)  $y = - \log ( x + 3 )$ 
D)  $y = \log ( x + 3 )$

Question 18

Determine the doubling time of the investment.
-4.72% APR compounded monthly

Accepted Answer

A)  22.07 years 
B)  11.77 years 
C)  14.71 years 
D)  29.43 years

Question 19

Solve the inequality graphically.
-$$\left( \frac { 1 } { 9 } \right) ^ { - x } > \left( \frac { 1 } { 5 } \right) ^ { - x }$$

Accepted Answer

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

Question 20

Find the exact solution to the equation.
-$$\log x = - 3$$

Accepted Answer

A)  $x = 30$ 
B)  $x = - 30$ 
C)  $x = \frac { 1 } { 310 }$ 
D)  $x = \frac { 1 } { 1000 }$

Exam 3: Exponential, Logistic, and Logarithmic Functions

Evaluate the logarithm. - $\log 100,000$

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. - $\log _ { 2 } 12 - \log _ { 2 } y$

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x) . - $f ( x ) = \ln ( x - 2 ) + 5 ; \quad g ( x ) = \ln x$

Match the function f with its graph. - $f ( x ) = \log _ { 5 } ( x - 1 )$

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. - $\frac { 1 } { 2 } \log _ { a } x + 3 \log _ { a } y - 2 \log _ { a } x$

Solve the problem. -Find the future value accumulated in an annuity after investing periodic payments of $134 for 8 years at an annual interest rate of 5%, with payments made and credited 4 times per year.

Determine the function which corresponds to the given graph. - $Determine the function which corresponds to the given graph. - The asymptote is x = - 2 . A) y = \ln ( x - 2 ) B) y = \ln x + 2 C) y = \ln ( x + 2 ) D) y = \ln x - 2$ The asymptote is $x = - 2$ .

Solve the problem. -Suppose you contribute to a fund that earns 5.5% annual interest. What should your quarterly payment be if you want to accumulate $190,000 in 18 years?

Match the function f with its graph. - $f ( x ) = \log _ { 5 } ( - x )$

Solve the problem. -Find the present value of a loan with an annual interest rate of 5.9% and periodic payments of $778.63 for a term of 7 years, with payments made and interest charged 12 times per year.

Provide an appropriate response. -The function $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. What is the annual interest rate?

Find the domain of the function. - $f ( x ) = \log _ { 4 } \left( 100 - x ^ { 2 } \right)$

Solve the equation. - $\log ( 3 + x ) - \log ( x - 2 ) = \log 2$

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $1,000, t = 4, r = 4%, compounded semiannually (k = 2)

Find the exponential function that satisfies the given conditions. -Initial population $= 1013$ , doubling every 6 hours

Determine the function which corresponds to the given graph. - $Determine the function which corresponds to the given graph. - The asymptote is x = - 3 A) y = \log ( 3 - x ) B) y = - \log ( x - 3 ) C) y = - \log ( x + 3 ) D) y = \log ( x + 3 )$ The asymptote is $x = - 3$

Determine the doubling time of the investment. -4.72% APR compounded monthly

Solve the inequality graphically. - $\left( \frac { 1 } { 9 } \right) ^ { - x } > \left( \frac { 1 } { 5 } \right) ^ { - x }$

Find the exact solution to the equation. - $\log x = - 3$

Exam 3: Exponential, Logistic, and Logarithmic Functions

Evaluate the logarithm. - log⁡100,000\log 100,000log100,000

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. - log⁡212−log⁡2y\log _ { 2 } 12 - \log _ { 2 } ylog2​12−log2​y

Graph the function. Describe its position relative to the graph of the indicated basic function. - f(x) =1−6−x; relative to f(x) =6xf ( x ) = 1 - 6 ^ { - x } ; \text { relative to } f ( x ) = 6 ^ { x }f(x) =1−6−x; relative to f(x) =6x

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x) . - f(x) =ln⁡(x−2) +5;g(x) =ln⁡xf ( x ) = \ln ( x - 2 ) + 5 ; \quad g ( x ) = \ln xf(x) =ln(x−2) +5;g(x) =lnx

Match the function f with its graph. - f(x) =log⁡5(x−1) f ( x ) = \log _ { 5 } ( x - 1 ) f(x) =log5​(x−1)

Solve the problem. -Find the future value accumulated in an annuity after investing periodic payments of $134 for 8 years at an annual interest rate of 5%, with payments made and credited 4 times per year.

Determine the function which corresponds to the given graph. - The asymptote is x=−2x = - 2x=−2 .

Solve the problem. -Suppose you contribute to a fund that earns 5.5% annual interest. What should your quarterly payment be if you want to accumulate $190,000 in 18 years?

Match the function f with its graph. - f(x) =log⁡5(−x) f ( x ) = \log _ { 5 } ( - x ) f(x) =log5​(−x)

Solve the problem. -Find the present value of a loan with an annual interest rate of 5.9% and periodic payments of $778.63 for a term of 7 years, with payments made and interest charged 12 times per year.

Provide an appropriate response. -The function f(x)=200(1+0.06/4)x−10.06/4f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }f(x)=2000.06/4(1+0.06/4)x−1​ describes the future value of a certain annuity. What is the annual interest rate?

Find the domain of the function. - f(x) =log⁡4(100−x2) f ( x ) = \log _ { 4 } \left( 100 - x ^ { 2 } \right) f(x) =log4​(100−x2)

Solve the equation. - log⁡(3+x) −log⁡(x−2) =log⁡2\log ( 3 + x ) - \log ( x - 2 ) = \log 2log(3+x) −log(x−2) =log2