Exam 3: Exponential and Logarithmic Functions

Let Q represent a mass of radioactive radium (²²⁶Ra) (in grams), whose half-life is 1599 years.The quantity of radium present after t years is $Q = 5 \left( \frac { 1 } { 2 } \right) ^ { t / 1599 }$ Determine the quantity present after 300 years.Round to the nearest hundredth of a gram.

Condense the expression $\frac { 1 } { 5 } \left[ \log _ { 4 } x + \log _ { 4 } 3 \right] - \left[ \log _ { 4 } y \right]$ to the logarithm of a single term.

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places. $f ( x ) = 3 ^ { - x }$

Solve the exponential equation algebraically.Approximate the result to three decimal places. $4 e ^ { x } = 33$

Write the logarithmic equation in exponential form. $\ln ( 295 ) = 5.687 \ldots$

A population growing at an annual rate r will triple in a time t given by the formula $t = \frac { \ln 3 } { r }$ .If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple?

Let Q represent a mass of radioactive plutonium $\left( { } ^ { 239 } \mathrm { Pu } \right)$ (in grams), whose half life is 24,100 years.The quantity of plutonium present after t years is $Q = 16 \left( \frac { 1 } { 2 } \right) ^ { t / 24,100 }$ .Determine the quantity present after 67,000 years.Round your answer to one decimal place.

Use the One-to-One Property to solve the following equation for x. $2 ^ { 3 x } = 128$

Identify the graph of the function. $f ( x ) = 3 - 5 ^ { x }$

Identify the x-intercept of the function $f ( x ) = 4 \ln ( x - 1 )$ .

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) $\log _ { 8 } \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 3 } }$

Use the properties of logarithms to rewrite and simplify the logarithmic expression. $\ln \left( \frac { 2 } { e ^ { 3 } } \right)$

Select the correct graph for the given function $y = \ln ( x + 2 )$

What is the value of the function $f ( x ) = 150 e ^ { 0.4 x }$ at $x = 2.3$ Round to 3 decimal places.

Write the exponential equation $e ^ { 3 / 2 } = 4.4817 \ldots$ in logarithmic form.

Solve for x: $5 ^ { - x / 3 } = 0.0052$ .Round to 3 decimal places.

Rewrite the exponential equation $5 ^ { - 3 } = \frac { 1 } { 125 }$ in logarithmic form.

Match the graph with its exponential function.

Use the properties of logarithms to simplify the expression. $9 ^ { \log _ { 9 } 17 }$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $f ( x ) = 2000 \left( 2 ^ { x } \right)$ $x = - 1.1$