Problem

The logistic growth function $\mathrm{P}(\mathrm{x})=\frac{90}{1+271 e^{-0.122 x}}$ models the percentage, $\mathrm{P}(\mathrm{x})$, of Americans who are $\mathrm{x}$ years old and have some coronary heart disease. Use this function to find the the percentage of 41-year olds who have some coronary heart disease. What is the percentage of 41 -year olds with some coronary heart disease? $\%$ (Round to one decimal place.)

Solution

Step 1 :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 and have some coronary heart disease.

Step 2 :We are asked to find the percentage of 41-year olds who have some coronary heart disease. This can be found by substituting \(x=41\) into the logistic growth function \(P(x)\) and calculating the result.

Step 3 :After calculation, we find that the percentage is approximately 31.9%.

Step 4 :So, the percentage of 41-year olds who have some coronary heart disease is approximately \(\boxed{31.9\%}\).

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Source: https://solvelyapp.com/problems/16780/

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