Exam 5: Inverse, Exponential, and Logarithmic Functions

Find the present value of the future value. - $\mathrm { S } ( \mathrm { t } ) = \mathrm { se } ^ { - 0.018 \mathrm { t } }$ , where s is the initial amount in grams and t is the time in years since this initial amount was present. If you have a 76-gram piece of this element, How many grams will you have 4 years from now? Round your answer to the nearest tenth of a Gram.

Solve the equation. Round to the nearest thousandth. - $2 ( 4 x - 2 ) = 22$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = 4 ^ { x }$ . Find $f ( 3 )$

Determine whether the statement is true or false. -If $\mathrm { f }$ is a one-to-one function and the graph of $\mathrm { f }$ lies completely within the first and fourth quadrants, then the graph of $\mathrm { f } ^ { - 1 }$ lies completely within the first and second quadrants.

Solve the problem. -Find the number of years for $10,800 to grow to $14,300 at 5% compounded quarterly. Round to the nearest tenth of a year.

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ - $\frac { 3 } { 7 } \log _ { b } 9 y + \frac { 7 } { 5 } \log _ { b } \left( 81 y ^ { 2 } \right)$

Find the value. Give an approximation to four decimal places. - $\log 0.0819$

Solve the problem. -If an earthquake measured 5.2 on the Richter scale, what was the approximate intensity of the earthquake in terms of $\mathrm { I } _ { 0 }$ ? Intensity on the Richter scale is $\log _ { 10 } \left( \mathrm { I } / \mathrm { I } _ { 0 } \right)$

Graph the function. Give the domain and range. - $f(x)=\log _{5} x$

Solve the equation and express the solution in exact form. - $\ln ( 4 x - 1 ) + \ln ( x - 1 ) = \ln 1$

Provide an appropriate response. -The graph of an exponential function with base a is given. Is a > 1 or is 0 < a < 1? Explain how you arrived at your answer. Give the domain and range of f. $f(x)=a^{x}$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." -{(4, 5), (7, 5), (1, 4)}