Chapter 5.1, Problem 10E

Special Rounding Instructions When you perform logistic regression, round the r value to three decimal places and the other parameters to two decimal places. Round all answers to two decimal places unless other-wise indicated.

Mortality Versus Age. One study of morality versus age used the following model to give the probability P of death from measles It contracted at age t years:

$P=\frac{1}{1+77.39e^{-0.08t}}$

Here we assume that t is at least $2$.

a. What is the limiting value for this logistic function? (Note: In other contexts, this would be known as the carrying capacity.)

b. Explain in practical terms the meaning of the limiting value you found in part a.

c. At what age does the model predict that mortality due to measles is $70\%$ ? (That is a value of $0.7$ for P.)