the logistic growth function $p(x)=\\frac{90}{1 + 271e^{-0.122x}}$ models the percentage, $p(x)$, of…

the logistic growth function $p(x)=\\frac{90}{1 + 271e^{-0.122x}}$ models the percentage, $p(x)$, of americans who are $x$ years old and have some coronary heart disease. use this function to find the the percentage of 67 - year olds who have some coronary heart disease. what is the percentage of 67 - year olds with some coronary heart disease? \n$\\square\\%$ (round to one decimal place.)

the logistic growth function $p(x)=\\frac{90}{1 + 271e^{-0.122x}}$ models the percentage, $p(x)$, of americans who are $x$ years old and have some coronary heart disease. use this function to find the the percentage of 67 - year olds who have some coronary heart disease. what is the percentage of 67 - year olds with some coronary heart disease? \n$\\square\\%$ (round to one decimal place.)

Answer

Explanation:

Step1: Substitute (x = 67) into the function

We have the logistic - growth function (P(x)=\frac{90}{1 + 271e^{-0.122x}}). Substitute (x = 67) into the function: [P(67)=\frac{90}{1+271e^{-0.122\times67}}] First, calculate the exponent: (-0.122\times67=-8.174) Then, calculate (e^{-8.174}). Using the formula (y = e^{x}), where (x=-8.174), we know that (e^{-8.174}=\frac{1}{e^{8.174}}\approx\frac{1}{3550.79}\approx0.000282)

Step2: Calculate the denominator

Calculate (1 + 271e^{-0.122\times67}). Substitute (e^{-0.122\times67}\approx0.000282) into the denominator: (1+271\times0.000282=1 + 0.076422=1.076422)

Step3: Calculate (P(67))

Now, calculate (P(67)=\frac{90}{1.076422}\approx83.6)

Answer:

(83.6%)