Exam 4: Exponential and Logarithmic Functions

Solve the problem. -A city is growing at the rate of $0.9 \%$ annually. If there were $3,619,000$ residents in the city in 1994 , find how many (to the nearest ten-thousand) are living in that city in 2000 . Use $y = 3,619,000 ( 2.7 ) { } ^ { 0.009 t }$ .

Graph the function. -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { - x }$ .

Solve the problem. -The rabbit population in a forest area grows at the rate of $5 \%$ monthly. If there are 150 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $y = 150 ( 2.7 ) ^ { 0.05 t }$ .

Find the domain of the logarithmic function. - $f ( x ) = \log _ { 9 } ( x + 1 ) ^ { 2 }$

Evaluate or simplify the expression without using a calculator. - $\log 10 ^ { 9 }$

Evaluate or simplify the expression without using a calculator. - $\ln \mathrm { e } ^ { 2 }$

Graph the function. -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = - e ^ { x }$ .

The graph of a logarithmic function is given. Select the function for the graph from the options. -

Evaluate or simplify the expression without using a calculator. - $10 ^ { \log 7 }$

Graph the function. -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { x } - 2$

$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$ -Find the accumulated value of an investment of $940 at 6% compounded annually for 6 years.

The graph of a logarithmic function is given. Select the function for the graph from the options. -

Solve the problem. -The function $\mathrm { f } ( \mathrm { x } ) = 600 ( 0.5 ) ^ { \mathrm { x } / 80 }$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $x$ is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 140 years. Round to the nearest whole number.

Approximate the number using a calculator. Round your answer to three decimal places. - $a ^ { 3.4 }$

Graph the function. -Use the graph of $\log _ { 4 } x$ to obtain the graph of $f ( x ) = 2 + \log _ { 4 } x$ .

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Graph the function. -Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = 5 - \log x$

Evaluate or simplify the expression without using a calculator. - $\log 0.001$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } \left( \frac { \sqrt { x } } { 125 } \right)$

Graph the function. -Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = \log x + 1$