Question 1

Find the exponential function that satisfies the given conditions.
-Initial value $= 38$, increasing at a rate of $8 \%$ per year

Accepted Answer

A)  $f ( t ) = 38 \cdot 8 ^ { t }$ 
B)  $f ( t ) = 38 \cdot 0.08 \mathrm { t }$ 
C)  $f ( t ) = 38 \cdot 1.08 ^ { t }$ 
D)  $f ( t ) = 8 \cdot 1.08 ^ { t }$

Question 2

Provide an appropriate response.
-$$\text { Explain how the graph of } y = 3 ^ { x + 2 } - 5 \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$$

Accepted Answer

The answer of Provide an appropriate response.
-\[\text { Explain how...

Question 3

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( - x ) + 10 ; g ( x ) = \ln x$$

Accepted Answer

A)  Reflect across the $y$-axis and translate 10 units to the right. 
B)  Reflect across the $x$-axis and translate 10 units down. 
C)  Reflect across the $y$-axis and translate 10 units up. 
D)  Reflect across the $x$-axis and translate 10 units to the right.

Question 4

Solve the problem.
-What would your monthly payment be for a 4-year $9000 car loan with an APR of 7.89%?

Accepted Answer

A)  $263.10 
B)  $306.95 
C)  $219.25 
D)  $175.40

Question 5

Find the exact solution to the equation.
-$$3 ( 12 - 3 x ) = 27$$

Accepted Answer

A)  $x = 9$ 
B)  $x = 3$ 
C)  $x = - 3$ 
D)  $x = 4$

Question 6

Determine the doubling time of the investment.
-$1100 at 7% compounded quarterly

Accepted Answer

A)  19.98 years 
B)  14.98 years 
C)  7.99 years 
D)  9.99 years

Question 7

Find the domain of the function.
-$$f ( x ) = 3 \log _ { 6 } \left( x ^ { 4 } \right)$$

Accepted Answer

A)  $( 3 , \infty )$ 
B)  $\left( \frac { 9 } { 2 } , \infty \right)$ 
C)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $( 0 , \infty )$

Question 8

Solve the problem.
-Suppose you contribute $75 per quarter into a fund that earns 14.4% annual interest. What is the value of your investment after 12 years?

Accepted Answer

A)  $12,081.74 
B)  $7434.92 
C)  $9293.65 
D)  $16,728.57

Question 9

Solve the problem.
-Find the annual percentage yield if $P is invested at 5.27% compounded continuously.

Accepted Answer

A)  9.47 % 
B)  8.12 % 
C)  6.76 % 
D)  5.41 %

Question 10

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.
-$\log _ { b } x + \log _ { b } y$

Accepted Answer

A)  $\log _ { b } ( x + y )$ 
B)  $\log _ { 2 b } ( x + y )$ 
C)  $\log _ { b } x y$ 
D)  $\log _ { 2 b } x y$

Question 11

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( 8 - x ) ; \quad g ( x ) = \ln x$$

Accepted Answer

A)  Reflect across the $y$-axis and then translate 8 units to the left. 
B)  Reflect across the $x$-axis and then translate 8 units to the left. 
C)  Reflect across the $y$-axis and then translate 8 units to the right. 
D)  Reflect across the $x$-axis and then translate 8 units to the right.

Question 12

Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function.
-$f(x)=\log _{1 / 8} x$

Accepted Answer

A)  Vertically shrink by a factor $\frac { 1 } { \ln 8 }$
 
B)  Reflect across the $x$-axis and shift up $( \ln 8 )$ units
 
C)  Shift down $( \ln 8 )$ units
 
D)  Reflect across the $x$-axis and $\text { vertically shrink by a factor } \frac{1}{\ln 8}$

Question 13

Solve the inequality graphically.
-$$5 ^ { - x } < 8 ^ { - x }$$

Accepted Answer

A)  $x > 1$ 
B)  $x  0$

Question 14

Find the logistic function that satisfies the given conditions.
-

Accepted Answer

A)  $f ( x ) = 1.8 \cdot 0.9 x$ 
B)  $f ( x ) = 2 \cdot 0.9 x$ 
C)  $f ( x ) = 2 \cdot 0.7 ^ { x }$ 
D)  $f ( x ) = 2 \cdot 1.1 ^ { x }$

Question 15

Solve the inequality graphically.
-$\left( \frac { 1 } { 8 } \right) ^ { x } < \left( \frac { 1 } { 7 } \right) ^ { x }$

Accepted Answer

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

Question 16

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

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 17

Decide if the function is an exponential function. If it is, state the initial value and the base.
-$$y = 9 ^ { 3 }$$

Accepted Answer

A)  Exponential Function; base $= 9$; initial value $= 0$ 
B)  Exponential Function; base $= 3$; initial value $= 0$ 
C)  Not an exponential function 
D)  Exponential Function; base $= 9$; initial value $= 1$

Question 18

Solve the problem.
-Find the future value accumulated in an annuity after investing periodic payments of $300 for 6 years at an annual interest rate of 7%, with payments made and credited 4 times per year.

Accepted Answer

A)  $8853.30 
B)  $15,935.95 
C)  $10,623.97 
D)  $5311.98

Question 19

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry,
boundedness, extrema, asymptotes, and end behavior.
-$$f ( x ) = \frac { 8 } { 1 + 3 e ^ { - x } }$$

Accepted Answer

The answer of Graph the function and analyze it for...

Question 20

Match the function with its graph.
-$$f ( x ) = \ln x ^ { 3 }$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Exam 3: Exponential, Logistic, and Logarithmic Functions

Find the exponential function that satisfies the given conditions. -Initial value $= 38$ , increasing at a rate of $8 \%$ per year

Provide an appropriate response. - $\text { Explain how the graph of } y = 3 ^ { x + 2 } - 5 \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x) . - $f ( x ) = \ln ( - x ) + 10 ; g ( x ) = \ln x$

Solve the problem. -What would your monthly payment be for a 4-year $9000 car loan with an APR of 7.89%?

Find the exact solution to the equation. - $3 ( 12 - 3 x ) = 27$

Determine the doubling time of the investment. -$1100 at 7% compounded quarterly

Find the domain of the function. - $f ( x ) = 3 \log _ { 6 } \left( x ^ { 4 } \right)$

Solve the problem. -Suppose you contribute $75 per quarter into a fund that earns 14.4% annual interest. What is the value of your investment after 12 years?

Solve the problem. -Find the annual percentage yield if $P is invested at 5.27% compounded continuously.

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. - $\log _ { b } x + \log _ { b } y$

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x) . - $f ( x ) = \ln ( 8 - x ) ; \quad g ( x ) = \ln x$

Solve the inequality graphically. - $5 ^ { - x } < 8 ^ { - x }$

Find the logistic function that satisfies the given conditions. - $Find the logistic function that satisfies the given conditions. - A) f ( x ) = 1.8 \cdot 0.9 x B) f ( x ) = 2 \cdot 0.9 x C) f ( x ) = 2 \cdot 0.7 ^ { x } D) f ( x ) = 2 \cdot 1.1 ^ { x }$

Solve the inequality graphically. - $\left( \frac { 1 } { 8 } \right) ^ { x } < \left( \frac { 1 } { 7 } \right) ^ { x }$

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

Decide if the function is an exponential function. If it is, state the initial value and the base. - $y = 9 ^ { 3 }$

Solve the problem. -Find the future value accumulated in an annuity after investing periodic payments of $300 for 6 years at an annual interest rate of 7%, with payments made and credited 4 times per year.

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = \frac { 8 } { 1 + 3 e ^ { - x } }$

Match the function with its graph. - $f ( x ) = \ln x ^ { 3 }$

Exam 3: Exponential, Logistic, and Logarithmic Functions

Find the exponential function that satisfies the given conditions. -Initial value =38= 38=38 , increasing at a rate of 8%8 \%8% per year

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) +10;g(x) =ln⁡xf ( x ) = \ln ( - x ) + 10 ; g ( x ) = \ln xf(x) =ln(−x) +10;g(x) =lnx

Solve the problem. -What would your monthly payment be for a 4-year $9000 car loan with an APR of 7.89%?

Find the exact solution to the equation. - 3(12−3x) =273 ( 12 - 3 x ) = 273(12−3x) =27

Determine the doubling time of the investment. -$1100 at 7% compounded quarterly

Find the domain of the function. - f(x) =3log⁡6(x4) f ( x ) = 3 \log _ { 6 } \left( x ^ { 4 } \right) f(x) =3log6​(x4)

Solve the problem. -Suppose you contribute $75 per quarter into a fund that earns 14.4% annual interest. What is the value of your investment after 12 years?

Solve the problem. -Find the annual percentage yield if $P is invested at 5.27% compounded continuously.

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⁡bx+log⁡by\log _ { b } x + \log _ { b } ylogb​x+logb​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⁡(8−x) ;g(x) =ln⁡xf ( x ) = \ln ( 8 - x ) ; \quad g ( x ) = \ln xf(x) =ln(8−x) ;g(x) =lnx

Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function. - f(x) =log⁡1/8xf(x) =\log _{1 / 8} xf(x) =log1/8​x

Solve the inequality graphically. - 5−x<8−x5 ^ { - x } < 8 ^ { - x }5−x<8−x

Find the logistic function that satisfies the given conditions. -

Solve the inequality graphically. - (18) x<(17) x\left( \frac { 1 } { 8 } \right) ^ { x } < \left( \frac { 1 } { 7 } \right) ^ { x }(81​) x<(71​) x