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Chapter 4: Problem 64
Would you prefer that your salary be modeled exponentially or logarithmically? Explain your answer.
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Describe a difference between exponential growth and logistic growth.
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 \(50 \% ?\)
Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log _{5}\left(\frac{\sqrt{x}}{25}\right)\)
The half-life of the radioactive element plutonium-239 is \(25,000\) years. If 16 grams of plutonium- 239 are initially present, how many grams are present after \(25,000\) years? \(50,000\) years? \(75,000\) years? \(100,000\) years? \(125,000\) years?
Use the exponential decay model for carbon- \(14, A=A_{0} e^{-0.000121 t}\) to solve Exercises \(19-20\) Skeletons were found at a construction site in San Francisco in \(1989 .\) The skeletons contained \(88 \%\) of the expected amount of carbon-14 found in a living person. In \(1989,\) how old were the skeletons?
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