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Chapter 4: Problem 94
Solve each equation. $$ 3^{x+2} \cdot 3^{x}=81 $$
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The function \(W(t)=2600\left(1-0.51 e^{-0.075 t}\right)^{3}\) models the mveight, \(W(t),\) in kilograms, of a female African elephant eat age \(t\) years. ( 1 kilogram \(\approx 2.2\) pounds) Use a graphing utility to graph the function. Then TRACE along the curve to estimate the age of an adult female elephant weighing 1800 kilograms.
If \(f(x)=\log _{b} x,\) show that $$ \frac{f(x+h)-f(x)}{h}=\log _{b}\left(1+\frac{h}{x}\right)^{\frac{1}{h}} h \neq 0 $$
Use the proof of the product rule in the appendix to prove the quotient rule.
Hurricanes are one of nature's most destructive forces. These low-pressure areas often have diameters of over 500 miles. The function \(f(x)=0.48 \ln (x+1)+27\) models the barometric air pressure, \(f(x),\) in inches of mercury, at a distance of \(x\) miles from the eye of a hurricane. Use this function to solve. Graph the function in a \([0,500,50]\) by \([27,30,1]\) viewing rectangle. What does the shape of the graph indicate about barometric air pressure as the distance from the eye increases?
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because the equations $$\log (3 x+1)=5 \text { and } \log (3 x+1)=\log 5$$ are similar, I solved them using the same method.
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