When the parameter r in the logistic formula is negative (resulting in a positive power of e), the logistic curve has a different shape. For example, the following formula gives the approximate number of deaths due to tuberculosis as a fraction of all deaths in the United Statest years after 1875. 0.13 T= 1+ 0.07e.0s (a) Make a graph of T versus t. Include dates up to 2000. т 0.15 0.15 0.10 0.10 0.05 0.05 20 40 60 80 100 120 20 40 60 80 100 120 0.15 0.15 0.10 0.10 0.05 0.05 20 40 60 80 100 120 20 40 60 80 100 120 (b) What is the limiting value of T?

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Chapter2: Second-order Linear Odes
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When the parameter r in the logistic formula is negative (resulting in a positive power of e), the logistic curve has a different shape. For example, the following formula gives the approximate
number of deaths due to tuberculosis as a fraction
all deaths in the United States t years after 1875.
0.13
T=
1+ 0.07e.05t
(a) Make a graph of T versus t. Include dates up to 2000.
T.
0.15
0.15
0.10
0.10
0.05
0.05
20
40
60
80
100
120
20
40
60
80
100
120
0.15
0.15
0.10
0.10
0.05
0.05
20
40
60
80
100
120
20
40
60
80
100
120
(b) What is the limiting value of T?
Explain in practical terms what this limiting value means.
O In the long run, 7% of people will die from tuberculosis.
O In the long run, 13% of people will die from tuberculosis.
O In the long run, everyone will die of tuberculosis.
O In the long run, 50% of people will die from tuberculosis.
O In the long run, very few people will die of tuberculosis.
() Estimate when the fraction of deaths due to tuberculosis was decreasing most rapidly. Give your answer accurate to the nearest decade (e.g., 1920).
Transcribed Image Text:When the parameter r in the logistic formula is negative (resulting in a positive power of e), the logistic curve has a different shape. For example, the following formula gives the approximate number of deaths due to tuberculosis as a fraction all deaths in the United States t years after 1875. 0.13 T= 1+ 0.07e.05t (a) Make a graph of T versus t. Include dates up to 2000. T. 0.15 0.15 0.10 0.10 0.05 0.05 20 40 60 80 100 120 20 40 60 80 100 120 0.15 0.15 0.10 0.10 0.05 0.05 20 40 60 80 100 120 20 40 60 80 100 120 (b) What is the limiting value of T? Explain in practical terms what this limiting value means. O In the long run, 7% of people will die from tuberculosis. O In the long run, 13% of people will die from tuberculosis. O In the long run, everyone will die of tuberculosis. O In the long run, 50% of people will die from tuberculosis. O In the long run, very few people will die of tuberculosis. () Estimate when the fraction of deaths due to tuberculosis was decreasing most rapidly. Give your answer accurate to the nearest decade (e.g., 1920).
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