One study of mortality versus age used the following model to give the probability P of death from measles if contracted at age t years.P = 1/1 + 77.39e−0.08tHere 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).The limiting value indicates that as age increases, the probability of death upon contracting measles at that age increases toward  or  %.(c) At what age does the model predict that mortality due to measles is 50%? (That is a value of 0.5 for P. Round your answer to two decimal places.)t =

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Asked Dec 3, 2019
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One study of mortality versus age used the following model to give the probability P of death from measles if contracted at age t years.

P = 
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).
The limiting value indicates that as age increases, the probability of death upon contracting measles at that age increases toward  or  %.

(c) At what age does the model predict that mortality due to measles is 50%? (That is a value of 0.5 for P. Round your answer to two decimal places.)
t = 
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Expert Answer

Step 1

(a) The formula for a logistic model is,

K
N -
1+be
1
Given logistic equation is P-
1+77.39e0.08
Comparing both the equation, K 1.
Thus, the limiting value of the logistic function is 1
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K N - 1+be 1 Given logistic equation is P- 1+77.39e0.08 Comparing both the equation, K 1. Thus, the limiting value of the logistic function is 1

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Step 2

(b)

Comparing the logistic model and given logistic equation, K = 1 and it represent that the maximum probability P of mortality due to measle...

max
Hence, the meaning of the limiting value you found in part (a) is the maximum
mortality due to measles could be 100%.
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max Hence, the meaning of the limiting value you found in part (a) is the maximum mortality due to measles could be 100%.

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