Exam 4: Exponential and Logarithmic Functions

Graph the function. - $y=\log _{1 / 4} x$ A) B) C) D)

Find the inverse of the function and state its domain and range . - $\{ ( - 3,4 ) , ( - 1,5 ) , ( 0,2 ) , ( 2,6 ) , ( 5,7 ) \}$

Solve the equation. - $\log _ { 5 } x = 2$

Find the value of the expression. -Let $\log _ { b } A = 5$ and $\log _ { b } B = - 4$ . Find $\log _ { b } B ^ { 2 }$ .

Solve the problem. Round your answer to three decimals. -How long will it take for an investment to triple in value if it earns 8.5% compounded continuously?

Write as the sum and/or difference of logarithms. Express powers as factors. - $\ln \left( \frac { ( x + 5 ) ( x - 2 ) } { ( x - 8 ) ^ { 4 } } \right) ^ { 4 / 3 } , \quad x > 2$

Solve the problem. -The logistic growth functi $f ( t ) = \frac { 800 } { 1 + 9.0 e ^ { - 0.16 t } }$ describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 15 Months?

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $4 ^ { 6 x } = 4.8$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 5 } x = 2$

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f(x)=+5 A) domain of $f : ( - \infty , \infty )$ ; range of $f : ( 2 , \infty )$ horizontal asymptote: $\mathrm { y } = 2$ B) domain of $f : ( - \infty , \infty )$ ; range of $f : ( 5 , \infty )$ horizontal asymptote: $\mathrm { y } = 5$ C) domain of $f : ( - \infty , \infty )$ ; range of $f : ( 2 , \infty )$ horizontal asymptote: $\mathrm { y } = 2$ D) domain of $f : ( - \infty , \infty )$ ; range of $f : ( 5 , \infty )$ horizontal asymptote: $\mathrm { y } = 5$

Solve the equation. - $3 ^ { - x } = \frac { 1 } { 9 }$

For the given functions f and g, find the requested composite function value. - $f ( x ) = 13 x ^ { 2 } - 4 x , \quad g ( x ) = 16 x - 10 ; \quad$ Find $( f \circ g ) ( 9 )$ .

Use transformations to graph the function. - $\text { Use the graph of } \log _ { 4 } x \text { to obtain the graph of } f ( x ) = \log _ { 4 } ( x - 1 ) \text {. }$ A) B) C) D)

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -The profit P for selling x items is given by the equation P(x) = 2x - 500. Express the sales amount x as a function of the profit P.

Solve the problem. -Which of the two rates would yield the larger amount in 1 year: 5.2% compounded monthly or 5.1% compounded daily?

Graph the function. - $f ( x ) = e ^ { - x }$ A) B) C) D)

Solve the problem. -If $5,000 is invested for 6 years at 5%, compounded continuously, find the future value.

Find the exact value of the logarithmic expression. - $\log _ { 10 } 1,000$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$

Use transformations to graph the function. - $\text { Use the graph of } \log _ { 4 } x \text { to obtain the graph of } f ( x ) = - 1 + \log _ { 4 } x \text {. }$ A) B) C) D)