Exam 5: Inverse, Exponential, and Logarithmic Functions

An everyday activity is described. Keeping in mind that an inverse operation "undoes" what an operation does, describe each inverse activity. -opening a door

Explain how the graph of can be obtained from the graph o -What is the range of the function $y = \log _ { 9 } x$ ?

Write an equivalent expression in exponential form. - $3 x - 12 = \log _ { x } 1$

Graph the exponential function using transformations where appropriate. - $f ( x ) = 2 ^ { x } + 2$

Choose the one alternative that best completes the statement or answers the question. -In a town whose population is 2500 , a disease creates an epidemic. The number $\mathrm { N }$ of people infected $\mathrm { t }$ days after the disease has begun is given by the function $\mathrm { N } ( \mathrm { t } ) = \frac { 2500 } { 1 + 20.3 \cdot \mathrm { e } ^ { - 0.8 \mathrm { t } } }$ . Find the number infected after 5 days.

Graph the function. Give the domain and range. - f(x)=(x+3)

Determine whether or not the function is one-to-one. - $f ( x ) = - 3.72$

Find the value. Give an approximation to four decimal places. - $\log 4944$

For the function as defined that is one-to-one, graph f and $\mathbf { f } ^ { - 1 }$ on the same axes. - $f ( x ) = \frac { 5 } { 2 } x + 3$

Find the value. Give an approximation to four decimal places. - $\ln 0.987$

Decide whether the pair of functions graphed are inverses. -

Choose the one alternative that best completes the statement or answers the question. -The number of books in a small library increases according to the function B $\mathrm { B } = 5200 \mathrm { e } ^ { 0.02 \mathrm { t } }$ , where t is measured in years. How many books will the library have after 2 years?

Provide an appropriate response. -Explain how the graph of $y = 2 ^ { x + 2 }- 1$ can be obtained from the graph o $y = 2 ^ { x }$

Provide an appropriate response. -Explain how the graph of $y = - 3 \left( \frac { 1 } { 4 } \right) ^ { x }$ can be obtained from the graph o $y = 4 ^ { x }$

Solve for the indicated variable. - $\mathrm { D } - \mathrm { D } _ { 0 } = \left( \mathrm { D } _ { 1 } - \mathrm { D } _ { 0 } \right) 10 - \mathrm { kt }$ , for $\mathrm { t }$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\log x ^ { 4 } = ( \log x ) ^ { 4 }$

Solve the equation. - $\left( \frac { 1 } { 5 } \right) ^ { x } = 625$

Determine whether or not the function is one-to-one. - $f ( x ) = \frac { 7 } { x + 3 }$

Write an equivalent expression in exponential form. - $\log 9 \sqrt { 910 } = x$

Choose the one alternative that best completes the statement or answers the question. -A lake is stocked with 557 fish of a new variety. The size of the lake, the availability of food, and the number of other fish restrict growth in the lake to a limiting value of 3481 . The population of fish in the lake after time $\mathrm { t }$ , in months, is given by the function $\mathrm { P } ( \mathrm { t } ) = \frac { 3481 } { 1 + 5.48 \mathrm { e } ^ { - 0.31 \mathrm { t } } }$ . After how many months will the population be 694 ?