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
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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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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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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