Exam 4: Exponential and Logarithmic Functions

Solve the problem. -There are currently 80 million cars in a certain country, decreasing by $7.3 \%$ annually. How many years will it take for this country to have 57 million cars? (Round to the nearest year.)

Solve the exponential equation. - $3^{7 \mathrm{x}}=243$

Graph the function. - $y=\ln (x+2)$

Solve the problem. -In the Smoky Mountains of Tennessee, the percent of moisture that falls as snow rather than rain is approximated by $\mathrm{P} \%=10.0 \ln \mathrm{h}-80$ , where $\mathrm{P}$ is the percent of snow moisture at an altitude $\mathrm{h}$ feet. What altitude corresponds to 2 percent snow moisture? Round to the nearest hundred feet.

Graph the function. - $y=\log 3 x+3$

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$ - $f(x)=-\left(3^{x}\right)$

Graph the function. - $f(x)=0.7^{x}$

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$ - $f(x)=6^{-x}$

Solve the problem. -The number of dislocated electric impulses per cubic inch in a transformer when lightning strikes is given by $D(x)=5400(4)^{x}$ , where $x$ is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at $\mathrm{x}=0$ and $\mathrm{x}=5$ .

Solve the exponential equation. - $7^{2 x}=7^{14.6}$

Solve the equation. - $\mathrm{e}^{0.226 \mathrm{x}}=8$

Provide an appropriate response. -What is the connection between e^x and ln x?

Solve the equation for $c$ .} - $10^{4 \mathrm{c}+1}=\mathrm{d}$

Graph the function. - $y=\log 1 / 2(x+4)$

Write the word or phrase that best completes each statement or answers the question. - $f(x)=a^{x}$ The graph of an exponential function with base a is given. Sketch the graph of $g(x)=a^{x}+2$ . Give the domain and range of $g$ .

Solve the equation for $s$ . - $\ln (5 \mathrm{~s}-5)=\mathrm{r}-2$

Graph the function. - $y=\log _{3} x$

Solve the problem. -An economist predicts that the buying power $B(x)$ of a dollar $x$ years from now will decrease according to the formula $\mathrm{B}(\mathrm{x})=0.42^{\mathrm{x}}$ . How much will today's dollar be worth in 5 years? Round the answer to the nearest cent.

Express the following in terms of $u$ and $v$ , where $u=\ln x$ and $v=\ln y$ . For example, $\ln x=3(\ln x)=3 u$ . - $\ln \left(x^{9} y^{17}\right)$

Provide an appropriate response. -In the given figure, the graphs of $y=a^{x}$ for $a=1.5,2.3,3.4,0.6,0.87,0.42$ are given. Identify the graph of $\mathrm{y}=2.3^{\mathrm{x}}$ .