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Exercises 56 and 57: The Gompertz differential equation dy = ky In (G) dt (where M and k are constants) was introduced in 1825 by the English mathematician Benjamin Gompertz and is still used today to model aging and mortality. 57. To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t) of rats alive at time t (in months) satisfies Eq. (2) with M = 204 and k = 0.15 month-' (Figure 16). Find P(t) [note that P(0) = 200] and determine the population after 20 months. Rat population P(1) 200 100+ 10 20 30 40 Time (months) FIGURE 16

Exercises 56 and 57: The Gompertz differential equation dy = ky In (G) dt (where M and k are constants) was introduced in 1825 by the English mathematician Benjamin Gompertz and is still used today to model aging and mortality. 57. To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t) of rats alive at time t (in months) satisfies Eq. (2) with M = 204 and k = 0.15 month-' (Figure 16). Find P(t) [note that P(0) = 200] and determine the population after 20 months. Rat population P(1) 200 100+ 10 20 30 40 Time (months) FIGURE 16

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Exercises 56 and 57: The Gompertz differential equation dy = ky In (G) dt (where M and k are constants) was introduced in 1825 by the English mathematician Benjamin Gompertz and is still used today to model aging and mortality. 57. To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t) of rats alive at time t (in months) satisfies Eq. (2) with M = 204 and k = 0.15 month-' (Figure 16). Find P(t) [note that P(0) = 200] and determine the population after 20 months. Rat population P(1) 200 100+ 10 20 30 40 Time (months) FIGURE 16
Transcribed Image Text:Exercises 56 and 57: The Gompertz differential equation dy = ky In (G) dt (where M and k are constants) was introduced in 1825 by the English mathematician Benjamin Gompertz and is still used today to model aging and mortality. 57. To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t) of rats alive at time t (in months) satisfies Eq. (2) with M = 204 and k = 0.15 month-' (Figure 16). Find P(t) [note that P(0) = 200] and determine the population after 20 months. Rat population P(1) 200 100+ 10 20 30 40 Time (months) FIGURE 16
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