Exam 4: Inverse, Exponential, and Logarithmic Functions

Solve the problem. -Use your graphing calculator to find how long it will take for $8000 invested at 4.8% per year compounded daily to triple in value. Find the answer to the nearest year. Use 365 days for a year.

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 5 } 6$

Solve the problem. -If $\mathrm { f } ( \mathrm { x } ) = 5 ^ { \mathrm { x } }$ , find $\mathrm { f } \left( \log _ { 5 } 8 \right)$ .

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 4.6 } 236$

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to solve the problem. -The function defined by f(x) = x + 2 was used to encode a message as: 15 3 22 10 9 7 16 11 23 21 Find the inverse function and determine the message.

Solve the equation. - $4 ( 7 - 3 x ) = \frac { 1 } { 16 }$

Write the word or phrase that best completes each statement or answers the question. - $\text { Why does } \log _ { a } a \text { always equal } 1 \text { for any valid base a? }$

Write the word or phrase that best completes each statement or answers the question. -The half-life of an element is $3.4 \times 10 ^ { 9 } \mathrm { yr }$ . How long does it take a sample of the element to decay to $\frac { 2 } { 5 }$ of its original mass? Use $A = A _ { 0 } ( 0.5 ) ( t / T )$ where $A _ { 0 }$ is the initial amount, $T$ is the half-life, and $t$ is the time. (Express results in scientific notation, rounded to the nearest hundredth.)

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { e } ^ { \mathrm { x } + \ln 3 } = 8 \mathrm { e } ^ { \mathrm { x } }$

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function. - $f ( x ) = \frac { - x } { x + 2 } ; [ - 8,8 ] \text { by } [ - 8,8 ]$

Solve the equation. Give the answer in exact form. - $e ^ { 2 x } - 8 e ^ { x } + 12 = 0$

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { a } \left( 4 x ^ { 3 } y \right)$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. -ex = 2x + 3

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

Write the word or phrase that best completes each statement or answers the question. -Suppose that $y = \frac { 2 - \log ( 100 - x ) } { 0.29 }$ can be used to calculate the number of years $y$ for x percent of a population of 222 web-footed sparrows to die. Approximate the percentage (to the nearest whole per cent) of web-footed sparrows that died after 5 years.

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 18$

Determine whether or not the function is one-to-one. - $f ( x ) = \sqrt { 36 - x ^ { 2 } }$

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

Write the word or phrase that best completes each statement or answers the question. -Write the algebraic equation which can be used to find the exact solution of $\log _ { 5 } 5 ( x - 2 ) =$ $\frac { - 20 } { x - 10 }$

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