Exam 5: Inverse, Exponential, and Logarithmic Functions

The number of books in a small library increases according to the functio $B = 5900 e ^ { 0.04 t }$ , where t is measured in years. How many books will the library have after 7 years?

models salinity of ocean water to depths of 1000 meters at a certain latitude. x is the depth in meters and f(x) is in grams of salt per kilogram of seawater. Approximate the depth (to the Nearest tenth of a meter) where the salinity equals 35.

Use the formula $\mathrm { D } = 10.0 \log \left( \mathrm { S } _ { \mathrm { S } } \mathrm { S } \right)$ , where the loudness of a sound in decibels is determined by $\mathrm { S }$ , the number of watt/ $/ \mathrm { m } ^ { 2 }$ produced by the soundwave, and $\mathrm { S } _ { 0 } = 1.00 \times 10 ^ { - 12 } \mathrm { watt } / \mathrm { m } ^ { 2 }$ . A certain noise produces $8.54 \times 10 ^ { - 5 }$ watt $/ \mathrm { m } ^ { 2 }$ of power. What is the decibel level of this noise? (Round to the nearest unit.)

Write in logarithmic form. - $10 ^ { 4 } = 10,000$

Find the value. Give an approximation to four decimal places. - $\ln ( 569 \times 24 )$

Find the domain and range of the inverse of the given function. - $f ( x ) = \sqrt [ 3 ] { 9 x - 7 }$

Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$ , as needed. -Find the $\mathrm { pH }$ if $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] = 1.0 \times 10 ^ { - 5 }$ .

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $7 e ^ { 2.4 x } = 45$

Write an equivalent expression in exponential form. - $x = 9 ^ { \log 9 } 2$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $\{ ( 19,5 ) , ( 10 , - 1 ) , ( - 19,7 ) \}$

Graph the exponential function using transformations where appropriate. - $f ( x ) = 2 ^ { x + 2 } - 1$

The graph of a function f is given. Use the graph to find the indicated value. - $f^{-1}(-3)$

Solve the equation and express the solution in exact form. - $\log 2 x = \log 5 + \log ( x - 2 )$

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Evaluate the logarithm. - $\log _ { 6 } \sqrt { 6 }$

What is the range of the function $y = \log _ { 10 } x$ ?

Decide whether the given functions are inverses. -

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - $\text { Let } f ( x ) = 2 ^ { x } \text {. Find } f ( 3.04 ) \text {. }$

Determine whether or not the function is one-to-one. -

Use the change of base rule to find the logarithm to four decimal places. -log9 0.60