Exam 4: Exponential and Logarithmic Functions

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 $\mathrm{h}$ in feet. Find the percent of moisture that falls as snow at an altitude of $4000 \mathrm{ft}$ . Round to the nearest percent.

Solve the problem. -The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by $\mathrm{D}(\mathrm{x})=3700(2)^{\mathrm{x}}$ , where $\mathrm{x}$ is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at $x=0$ and $x=4$ .

Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers. - $\ln (10 x+1)+\ln (x+8)$

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. Is a $>1$ or is $0<a<1$ ? Explain how you arrived at your answer. Give the domain and range of $\mathrm{f}$ .

Solve the problem. -The intensity of a certain noise is 1.24 . How loud, in decibels, is this sound level? Use the formula $\mathrm{D}=10 \log \left(\mathrm{I} / \mathrm{I}_{0}\right)$ , where $\mathrm{I}_{0}=10^{-16} \mathrm{~W} / \mathrm{cm}^{2}$ . (Round to the nearest decibel.)

Solve the problem. -Use a graphing calculator to predict about how many books will have been read in the eighth grade.

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. - $\ln \sqrt{8 \mathrm{t}^{4} \mathrm{v}^{2}}$

Solve the problem. -In the formula $\mathrm{N}=\mathrm{Ie}^{\mathrm{kt}}, \mathrm{N}$ is the number of items in terms of an initial population $\mathrm{I}$ at a given time $t$ and $k$ is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a certain country to double if its annual growth rate is $6.7 \%$ ? Round to the nearest year.

without graphing, describe the shape of the graph of the function and complete the ordered pairs $(0,1)$ and $(1$ , $) .$ - $f(x)=0.6^{x}$

Solve the problem. -The population growth of an animal species is described by $F(t)=200+50 \log _{3}(2 t+1)$ where $t$ is measured in months. Find the population of this species in an area $40 \mathrm{month}(\mathrm{s})$ after the species is introduced.

Solve the problem. -Use the formula $P=I e^{k t}$ . A bacterial culture has an initial population of 500. If its population grows to 7000 in 6 hours, what will it be at the end of 8 hours?

Graph the function. - $y=\log _{2}-x$

Solve the equation. - $\ln (2 x-3)=\ln 15-\ln (x-5)$

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

Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. - $\log \frac{3 x}{5 y}$

Provide an appropriate response. -The graph of an exponential function is given. Which of the following is the correct equation of the function?

Classify the function as a linear, quadratic, or exponential. - $f(x)=8 \cdot 54 x^{2}-3$

Find an exponential function of theform $P(t) = y_{0} e^{k t}$ to model the given data. -Under ideal conditions, a population of rabbits has an exponential growth rate of $11.6 \%$ per day. Consider an initial population of 900 rabbits. Find the exponential growth function.

Classify the function as a linear, quadratic, or exponential. - $f(x)=(x-4)(x+9)$

Convert to exponential form. - $\log 0.000001=-6$