91Ó°ÊÓ

Evaluate the function at the indicated value of \(x .\) Round your result to three decimal places. $$f(x)=250 e^{0.05 x} \quad x=20$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$3^{x^{2}}=7^{6-x}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$e^{2 x}-4 e^{x}-5=0$$

In Exercises \(37-58,\) use the properties of logarithms to expand the expression as a sum, difference, and or constant multiple of logarithms. (Assume all variables are positive.) $$\log _{8} x^{4}$$

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=e^{x}$$

IQ Scores The IQ scores for a sample of a class of returning adult students at a small northeastern college roughly follow the normal distribution $$y=0.0266 e^{-(x-100)^{2} / 450}, \quad 70 \leq x \leq 115$$ where \(x\) is the IQ score. (a) Use a graphing utility to graph the function. (b) From the graph in part (a), estimate the average IQ score of an adult student.

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=e^{-x}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$e^{2 x}-5 e^{x}+6=0$$

In Exercises \(37-58,\) use the properties of logarithms to expand the expression as a sum, difference, and or constant multiple of logarithms. (Assume all variables are positive.) $$\log _{10} \frac{y}{2}$$

Education The amount of time (in hours per week) a student utilizes a math- tutoring center roughly follows the normal distribution $$y=0.7979 e^{-(x-5.4)^{2} / 0.5}, \quad 4 \leq x \leq 7$$ where \(x\) is the number of hours. (a) Use a graphing utility to graph the function. (b) From the graph in part (a), estimate the average number of hours per week a student uses the tutoring center.