Exam 3: Exponential and Logarithmic Functions

Determine whether the scatter plot below could best be modeled by a linear model, a quadratic model, an exponential model, a logarithmic model, or a logistic model.

Identify the graph of the function. $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { 1 - x }$

The atmospheric pressure decreases with increasing altitude. At sea level, the average air pressure is approximately $1.03323$ kilograms per square centimeter, and this pressure is called one atmosphere. Variations in weather conditions cause changes in the atmospheric pressure of up to $\pm 5$ percent. The table below shows the pressures $p$ (in atmospheres) for various altitudes $h$ (in kilometers). Use the regression feature of a graphing utility to find the logarithmic model $h = a + b \ln p$ for the data. Use the model to estimate the altitude at which the pressure is $0.28$ atmosphere. Round your answer to two decimal places.

Evaluate the logarithm $\log _ { 7 } 126$ using the change of base formula. Round to 3 decimal places.

Match the function $y = 3 + \ln ( x + 2 )$ with its graph. Graph I: Graph II: Graph III: Graph IV: Graph V:

Solve the logarithmic equation below algebraically. $\ln ( x - 5 ) = \ln ( x + 1 ) - \ln ( x - 9 )$

Solve the logarithmic equation below algebraically. $\ln ( x + 3 ) = \ln ( x + 1 ) - \ln ( x + 7 )$

A conservation organization releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 900 animals and that the growth of the herd will follow the logistic curve $p ( t ) = \frac { 900 } { 1 + 10 e ^ { - 0.1656 t } }$ , where $t$ is measured in months. What is the population after 8 months? Round your answer to the nearest animal.

Find the exact value of $\log _ { 4 } 12 - \log _ { 4 } 3$ without using a calculator.

Condense the expression below to the logarithm of a single quantity. $4 [ \ln x - \ln ( x + 4 ) - \ln ( x - 4 ) ]$

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $\ln \left( x ^ { 2 } + 6 \right) = 5$

Solve the logarithmic equation below algebraically. Round your result to three decimal places. $\log _ { 9 } 4 x - \log _ { 9 } ( 1 + \sqrt { x } ) = 2$

Solve for $x : 5 ^ { - x / 2 } = 0.0052$ . Round to 3 decimal places.

Condense the expression $\log _ { 5 } x + \log _ { 5 } 7$ to the logarithm of a single term.

Identify the graph that represents the function. $y = \ln \frac { 1 } { x + 1 }$

Find the exact value of $\log _ { 5 } \sqrt [ 3 ] { 25 }$ without using a calculator.

Find the domain of the function below. $f ( x ) = \sqrt { \ln ( x + 2 ) }$

Solve the exponential equation below algebraically. $e ^ { - x ^ { 2 } } = e ^ { 2 x ^ { 2 } - 9 x }$

Identify the $x$ -intercept of the function $f ( x ) = 3 \ln ( x - 4 )$ .

Match the function $y = 1 + \ln ( x + 2 )$ with its graph. Graph I: Graph II: Graph III: Graph IV: Graph V: