Exam 5: Inverse, Exponential, and Logarithmic Functions

The atmospheric pressure at a given altitude is given by $y=14.7 e^{-.0000385 x}$ , where $y$ is the atmospheric pressure in pounds per square inch and $x$ is the altitude, in feet. Match each question with one of the solutions A, B, C, or D. -What is the atmospheric pressure at an altitude of 10 feet?

Consider the equation $\log _{3} x+\log _{3}(x-8)=2$ . (a) Solve the equation analytically. If there is an extraneous value, what is it? (b) To support the solution in part (a), we may graph $y_{1}=\log _{3} x+\log _{3}(x-8)-2$ and find the $x$ -intercept. Write an expression for $y_{1}$ using the change-of-base rule with base 10 , and graph the function to support the solution from part (a). (c) Use the graph to solve the inequality $\log _{3} x+\log _{3}(x-8)<2$ .

Solve the equation $16^{2 x-6}=\left(\frac{1}{8}\right)^{4 x-2}$ analytically.

Match each equation with its graph - $y=\left(\frac{1}{10}\right)^{x}$