Exam 9: Logarithmic and Exponential Functions

Solve the problem. -Yearly sales of an electronic device S(t), in millions of dollars, tyears after 2009 can be estimated by $\mathrm{S}(\mathrm{t})=200 \cdot 3^{\mathrm{t}}$ What is the doubling time for the yearly sales? Round your answer to the nearest tenth.

The growth in the population of a certain rodent at a dump site can be modeled by the exponential function $\mathrm{A}(\mathrm{t})=320 \mathrm{e}^{0.025 \mathrm{t}}$ , where $\mathrm{t}$ is the number of years since 1986. Estimate the rodent population in the year 2000.

Rewrite as the sum of two or more logarithms using the product rule for logarithms. A ssume all variables represent positive real numbers. - $\log _{6}(7 x)$

Solve. - $\log _{13}\left(\mathrm{x}^{2}-3 \mathrm{x}-27\right)=0$

Find the specified domain -For $f(x)=\frac{1}{x-4}$ and $g(x)=\frac{3}{x}$ , what is the domain of $f \circ g$ ?

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=-2 x, g(x)=10 x-5$ Find $(f \cdot g)(x)$ .

Solve. Round to the nearest thousandth, if necessary - $\mathrm{e}^{2 \mathrm{x}}=5$

Compute the compound interest. -Andrea Gilford's savings account has a balance of $\$ 916$ . After 6 years, what will the amount of interest be at $5 \%$ compounded annually? Round to the nearest dollar.

Compute the compound interest. -How long will it take for $\$ 7700$ to grow to $\$ 27,200$ at an interest rate of $10.9 \%$ if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Expand. A ssume that all variables represent positive real numbers. - $\log _{4}\left(\frac{\sqrt[9]{17}}{n^{2} m}\right)$

Evaluate. Round to the nearest thousandth, if necessary. - $\log \left(\frac{1}{1000}\right)$

Solve. - $\log _{4} \mathrm{x}=5$

A city is growing at the rate of $0.8 \%$ annually. If there were $5,316,000$ residents in the city in 1995 , find how many (to the nearest ten- thousand) were living in that city in 2000 . Use $\mathrm{y}=5,316,000(2.7)^{0.008 t}$

For the piecewise function $f(x)=\left\{\begin{array}{ll}x+3 & \text { if } x \leq-4 \\ -2 x+9 & \text { if } x>-4\end{array}\right.$ , find $(f \circ f)(-6)$ .

Graph f(x). State the domain, range, and horizontal asymptote of the function - $f(x)=\left(\frac{1}{2}\right)^{x+2}+1$

Solve the equation. - $\log 2 \mathrm{x}=\log 4+\log (\mathrm{x}-3)$

Use the horizontal-line test to determine whether the function is one to one. -

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=\frac{1}{3} x+9$

Evaluate. Round to the nearest thousandth, if necessary. - $\log 0.0624$

Rewrite in exponential form. - $\log _{2} 1=0$