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Chapter 12: Problem 7
Write each equation in its equivalent exponential form. $$\log _{6} 216=y$$
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The function \(W(t)=2600\left(1-0.51 e^{-0.075 t}\right)^{3}\) models the weight, \(W(t),\) in kilograms, of a female African elephant at age \(t\) years. (1 kilogram \(\approx 2.2\) pounds) Use a graphing utility to graph the function. Then \([\text { TRACE }]\) along the curve to estimate the age of an adult female elephant weighing 1800 kilograms.
The loudness level of a sound, \(D,\) in decibels, is given by the formula $$D=10 \log \left(10^{12} I\right)$$ where I is the intensity of the sound, in watts per meter \(^{2} .\) Decibel levels range from \(0,\) a barely audible sound, to \(160,\) a sound resulting in a nuptured eardrum. Use the formula to solve Exercises. The sound of a blue whale can be heard 500 miles away, reaching an intensity of \(6.3 \times 10^{6}\) watts per meter? Determine the decibel level of this sound. At close range, can the sound of a blue whale rupture the human eardrum?
Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I expanded \(\log _{4} \sqrt{\frac{x}{y}}\) by writing the radical using a rational exponent and then applying the quotient rule, obtaining \(\frac{1}{2} \log _{4} x-\log _{4} y\)
Complete the table for a savings account subject to n compounding periods per year \(\left[A=P\left(1+\frac{r}{n}\right)^{n t}\right]\) Round answers to one decimal place. $$\begin{array}{l|c|l|l|l} \hline \begin{array}{l} \text { Amount } \\ \text { Invested } \end{array} & \begin{array}{l} \text { Number of } \\ \text { Compounding } \\ \text { Periods } \end{array} & \begin{array}{l} \text { Annual Interest } \\ \text { Rate } \end{array} & \begin{array}{l} \text { Accumulated } \\ \text { Amount } \end{array} & \begin{array}{l} \text { Time } t \\ \text { in Years } \end{array} \\ \hline \$ 1000 & 360 & & \$ 1400 & 2 \\ \hline \end{array}$$
Graph \(f\) and \(g\) in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of \(f\). $$f(x)=\ln x, g(x)=\ln x+3$$
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