Question

The logistic growth function

P(x) = 90/1+271e⁻⁰.122x
models the percentage, P(x), of Americans who are x years old with some coronary heard disease.
QUESTION: What percentage of 80-year-olds have some coronary heart disease?

Answer 1

To calculate the percentage of 80-year-olds with coronary heart disease, substitute x=80 into the function P(x) = 90 / (1 + 271e^-0.122x). The result is approximately 88.6%.

Step-by-step explanation:

The question involves calculating the percentage of 80-year-olds with some coronary heart disease using the logistic growth function provided as P(x) = 90 / (1 + 271e-0.122x).

To find the percentage for 80-year-olds, we substitute x with 80 into the function:

P(80) = 90 / (1 + 271e-0.122 × 80)

Calculating the exponential part first:

e-0.122 × 80 ≈ e-9.76

≈ 0.000057416

Now, plug this value into the logistic function:

P(80) ≈ 90 / (1 + 271 × 0.000057416)

≈ 90 / (1 + 0.015564)

≈ 90 / 1.015564

≈ 88.604

Therefore, approximately 88.6% of Americans who are 80 years old have some coronary heart disease.