Exam 4: Exponential and Logarithmic Functions

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\frac { 1 } { 2 } \log _ { 9 } x + \log _ { 9 } y$

Use Compound Interest Formulas Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$ -Find the accumulated value of an investment of $900 at 10% compounded quarterly for 5 years.

Solve the problem. -The function $\mathrm { D } ( \mathrm { h } ) = 9 \mathrm { e } ^ { - 0.4 \mathrm {~h} }$ can be used to determine the milligrams $\mathrm { D }$ of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after 11 hours?

Solve the problem. -The $\mathrm { pH }$ of a solution ranges from 0 to 14 . An acid has a pH less than 7 . Pure water is neutral and has a pH of 7 . The $\mathrm { pH }$ of a solution is given by $\mathrm { pH } = - \log \mathrm { x }$ where $\mathrm { x }$ represents the concentration of the hydrogen ions in the solution in moles per liter. Find the hydrogen ion concentration if the $\mathrm { pH } = 5$ .

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

Approximate the number using a calculator. Round your answer to three decimal places. - $2 ^ { \sqrt { 3 } }$

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

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

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $e ^ { x + 3 } = 6$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } \sqrt { 3 x }$

Write the equation in its equivalent logarithmic form. - $13 ^ { 2 } = y$

Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 3 } ( x + 6 ) + \log _ { 3 } ( x - 6 ) - \log _ { 3 } x = 2$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $e ^ { x + 6 } = 3$

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $2 \log x - \log 4 = \log 169$

Solve the problem. -The population of a particular country was 22 million in 1984 ; in 1995, it was 34 million. The exponential growth function $\mathrm { A } = 22 \mathrm { e } ^ { \mathrm { kt } }$ describes the population of this country t years after 1984 . Use the fact that 11 years after 1984 the population increased by 12 million to find $\mathrm { k }$ to three decimal places.

Find the domain of the logarithmic function. - $f ( x ) = \log \left( \frac { x + 9 } { x - 8 } \right)$

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

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { b } \left( \frac { x y ^ { 4 } } { z ^ { 2 } } \right)$

Solve the problem. -The logistic growth function $\mathrm { f } ( \mathrm { t } ) = \frac { 82,000 } { 1 + 2732.3 \mathrm { e } ^ { - 1.4 \mathrm { t } } }$ models the number of people who have become ill with a particular infection t weeks after its initial outbreak in a particular community. What is the limiting size of the population that becomes ill?

Evaluate the expression without using a calculator. - $\log _ { 16 } 4$