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Chapter 4: Problem 93
Solve each equation. $$5^{2 x} \cdot 5^{4 x}=125$$
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The logistic growth function $$ P(x)=\frac{90}{1+271 e^{-0.122 x}} $$ models the percentage, \(P(x),\) of Americans who are \(x\) years old with some coronary heart disease. Use the function to solve Exercises \(43-46\) At what age is the percentage of some coronary heart disease \(50 \% ?\)
Describe the following property using words: \(\log _{b} b^{x}=x\).
The logistic growth function $$ P(x)=\frac{90}{1+271 e^{-0.122 x}} $$ models the percentage, \(P(x),\) of Americans who are \(x\) years old with some coronary heart disease. Use the function to solve Exercises \(43-46\) At what age is the percentage of some coronary heart disease \(70 \% ?\)
Use the exponential growth model, \(A=A_{0} e^{k t},\) to show that the time it takes a population to double (to grow from \(A_{0}\) to \(\left.2 A_{0}\right)\) is given by \(t=\frac{\ln 2}{k}\)
Without using a calculator, find the exact value of $$\frac{\log _{3} 81-\log _{\pi} 1}{\log _{2 \sqrt{2}} 8-\log 0.001}$$
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