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25. The data in the table in Fig. 2.1.7 are given for a certain population P(t) that satisfies the logistic equation in (3). (a) What is the limiting population M? (Suggestion: Use the approximation P(t + h) – P(t – h) P'(1) = 2h with h = 1 to estimate the values of P'(t) when P = 25.00 and when P = 47.54. Then substitute these values in the logistic equation and solve for k and M .) (b) Use the values of k and M found in part (a) to determine when P = 75. (Suggestion: Take t = 0 to correspond to the year 1925.) Year P (millions) 1924 24.63 1925 25.00 1926 25.38 1974 47.04 1975 47.54 1976 48.04 FIGURE 2.1.7. Population data for Problem 25.

25. The data in the table in Fig. 2.1.7 are given for a certain population P(t) that satisfies the logistic equation in (3). (a) What is the limiting population M? (Suggestion: Use the approximation P(t + h) – P(t – h) P'(1) = 2h with h = 1 to estimate the values of P'(t) when P = 25.00 and when P = 47.54. Then substitute these values in the logistic equation and solve for k and M .) (b) Use the values of k and M found in part (a) to determine when P = 75. (Suggestion: Take t = 0 to correspond to the year 1925.) Year P (millions) 1924 24.63 1925 25.00 1926 25.38 1974 47.04 1975 47.54 1976 48.04 FIGURE 2.1.7. Population data for Problem 25.

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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25. The data in the table in Fig. 2.1.7 are given for a certain population P(t) that satisfies the logistic equation in (3). (a) What is the limiting population M? (Suggestion: Use the approximation P(t + h) – P(t – h) P'(1) = 2h with h = 1 to estimate the values of P'(t) when P = 25.00 and when P = 47.54. Then substitute these values in the logistic equation and solve for k and M .) (b) Use the values of k and M found in part (a) to determine when P = 75. (Suggestion: Take t = 0 to correspond to the year 1925.) Year P (millions) 1924 24.63 1925 25.00 1926 25.38 1974 47.04 1975 47.54 1976 48.04 FIGURE 2.1.7. Population data for Problem 25.
Transcribed Image Text:25. The data in the table in Fig. 2.1.7 are given for a certain population P(t) that satisfies the logistic equation in (3). (a) What is the limiting population M? (Suggestion: Use the approximation P(t + h) – P(t – h) P'(1) = 2h with h = 1 to estimate the values of P'(t) when P = 25.00 and when P = 47.54. Then substitute these values in the logistic equation and solve for k and M .) (b) Use the values of k and M found in part (a) to determine when P = 75. (Suggestion: Take t = 0 to correspond to the year 1925.) Year P (millions) 1924 24.63 1925 25.00 1926 25.38 1974 47.04 1975 47.54 1976 48.04 FIGURE 2.1.7. Population data for Problem 25.
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