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Chapter 3: Problem 63
Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$5^{x}=212$$
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Students in a mathematics class took an exam and ther took a retest monthly with an equivalent exam. The average scores for the class are given by the human memory model \(f(t)=80-17 \log (t+1), \quad 0 \leq t \leq 12\) where \(t\) is the time in months.(a) Use a graphing utility to graph the model over the specified domain. (b) What was the average score on the original \(\operatorname{exam}(t=0) ?\)
Population The time \(t\) (in years) for the world population to double when it is increasing at a continuous rate of \(r\) is given by \(t=(\ln 2) / r\) (a) Complete the table and interpret your results. \begin{tabular}{|l|l|l|l|l|l|l|}\hline\(r\) & 0.005 & 0.010 & 0.015 & 0.020 & 0.025 & 0.030 \\\\\hline\(t\) & & & && &..\begin{array}{|l|l|l|l|l|l|l|} \hline r & 0.005 & 0.010 & 0.015 & 0.020 & 0.025 & 0.030 \\ \hline t & & & & & & \\ \hline \end{array}
Using the One-to-One Property In Exercises \(73-76,\) use the One-to-One Property to solve the equation for \(x\). \(\ln \left(x^{2}-x\right)=\ln 6\)
Solve the equation algebraically. Round your result to three decimal places. Verify your answer using a graphing utility. $$e^{-2 x}-2 x e^{-2 x}=0$$
Use a graphing utility to graph the functions \(y_{1}=\ln x-\ln (x-3)\) and \(y_{2}=\ln \frac{x}{x-3}\) in the same viewing window. Does the graphing utility show the functions with the same domain? If so, should it? Explain your reasoning.
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