Exam 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. -Larry has $2,000 to invest and needs $2,500 in 13 years. What annual rate of return will he need to get in order to accomplish his goal? (Round your answer to two decimals.)

The function f is one-to-one. Find its inverse. - $f ( x ) = \sqrt [ 3 ] { x + 5 }$

Write the word or phrase that best completes each statement or answers the question. -At a rock concert by The Who, the music registered a loudness level of 120 decibels. The human threshold of pain due to sound averages 130 decibels. Compute the ratio of the intensities associated with these two loudness level to determine by how much the intensity of a sound that crosses the human threshold of pain exceeds that of this particular rock concert.

Decide whether the composite functions, f ° g and g ° f, are equal to x. - $f ( x ) = \frac { 1 } { x } , g ( x ) = x$

Graph the function. - $f(x)=-1-\ln x$

Approximate the value using a calculator. Express answer rounded to three decimal places. - $5 \sqrt { 7 }$

For the given functions f and g, find the requested composite function value. - $f ( x ) = 5 x + 8 , \quad g ( x ) = - 1 / x ; \quad$ Find $( g \circ f ) ( 3 )$

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Write the word or phrase that best completes each statement or answers the question. - $\log _ { ( 2 / 3 ) } 19$

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. - $6 \frac { 1 } { 4 } \%$ compounded monthly

Write the word or phrase that best completes each statement or answers the question. - $\pi ^ { x + 1 } = e ^ { 2 x }$

Solve the problem. -The function $f ( x ) = 1 + 1.6 \ln ( x + 1 )$ models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where $x$ is the number of consecutive days the basketball player has practiced for two hours. After how many days of practice can the basketball player make an average of 7 consecutive free throws?

Solve the equation. - $\log ( x + 5 ) = \log ( 4 x - 4 )$

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - $f ( x ) = \frac { x } { x + 7 } ; \quad g ( x ) = \frac { 7 } { x + 5 }$

Graph the function. - $f(x)=2-e^{-0.95 x}$

Solve the equation. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 8$

Graph the function. - $f(x)=2 e^{x}$

Write the word or phrase that best completes each statement or answers the question. -A fully cooked turkey is taken out of an oven set at $200 ^ { \circ } \mathrm { C }$ (Celsius) and placed in a sink of chilled water of temperature $4 ^ { \circ } \mathrm { C }$ . After 3 minutes, the temperature of the turkey is measured to be $50 ^ { \circ } \mathrm { C }$ . How long (to the nearest minute) will it take for the temperature of the turkey to reach $15 ^ { \circ } \mathrm { C }$ ? Assume the cooling follows Newton Law of Cooling: $\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } } .$ (Round your answer to the nearest minute.)

Find the exact value of the logarithmic expression. - $\log _ { 5 } \sqrt { 5 }$

Choose the one alternative that best completes the statement or answers the question. - $\log \left( 1 - \frac { 1 } { x ^ { 3 } } \right)$