Exam 5: Inverse, Exponential, and Logarithmic Functions

Solve the problem. -Suppose $f ( x ) = 34.1 + 1.3 \log ( x + 1 )$ 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 36 .

Graph the exponential function using transformations where appropriate. - $f ( x ) = 3 ^ { x + 1 }$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ - $\frac { 1 } { 3 } \log _ { 3 } x ^ { 6 } + \frac { 1 } { 6 } \log _ { 3 } x ^ { 6 } - \frac { 1 } { 9 } \log _ { 3 } x$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $5 ( x + 1 ) = 22.00$

Graph the function. - $f(x)=3^{-x}$

Graph the exponential function using transformations where appropriate. - $f ( x ) = 4 ^ { x + 1 } - 4$

Determine the function value. -Suppose $f ( x ) = \log _ { a } x$ and $f ( 5 ) = 2$ . Find $f ( 25 )$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = \frac { 4 } { x + 7 }$

Write an equivalent expression in exponential form. - $\log _ { 10 } 0.1 = - 1$

Decide whether the given functions are inverses. - =\{(3,6),(3,3),(0,8)\} g=\{(3,3),(8,0),(6,6)\}

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = 2 ^ { x }$ . Find $f ( 2.28 )$ .

Choose the one alternative that best completes the statement or answers the question. -An economist predicts that the buying power $\mathrm { B } ( \mathrm { x } )$ of a dollar $\mathrm { x }$ years from now will decrease according to the formula $\mathrm { B } ( \mathrm { x } ) = 0.09 \mathrm { x }$ . How much will today's dollar be worth in 2 years? Round the answer to the nearest cent.

Find the value. Give an approximation to four decimal places. - $\log ( 204 \times 27 )$

Find the domain and range of the inverse of the given function. - $f ( x ) = 9 x + 9$

Find the present value of the future value. - $P = \left( \frac { 1 } { 2 } \right) ^ { t / 3.0 }$ The half-life of Cesium 134m is 3.0 hours. If the formula gives the percent (as a decimal) remaining after time t (in hours), sketch P versus t.

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ - $\frac { 3 } { 4 } \log _ { a } \left( p ^ { 2 } q ^ { 8 } \right) - \frac { 1 } { 2 } \log _ { a } \left( p ^ { 5 } q ^ { 2 } \right)$

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { a } \left( 4 x ^ { 5 } y \right)$

Choose the one alternative that best completes the statement or answers the question. -Use the formula $\mathrm { D } = 10.0 \log \left( \mathrm { S } / \mathrm { S } _ { 0 } \right)$ , 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 $\mathrm { S } _ { 0 } = 1.00 \times 10 ^ { - 12 }$ watt $/ \mathrm { m } ^ { 2 }$ . A certain noise produces $8.34 \times 10 ^ { - 5 } \mathrm { watt } / \mathrm { m } ^ { 2 }$ of power. What is the decibel level of this noise? (Round to the nearest unit.)

Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] , \text {as }$ needed. -Find the $\mathrm { pH }$ if $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] = 1.0 \times 10 ^ { - 4 }$ .

Explain how the graph of can be obtained from the graph o -Give a definition for the following term: Logarithmic function .