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Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy (0.4 + sin t) dt || 4 NOTE: Round your answers to two decimal places. a) If y(0) 1, find (or estimate) the time T at which the population || has doubled. Choose other initial conditions and determine whether the doubling time ↑ depends on the initial population. The doubling time is 7 = The doubling time Choos depend on the initial population one ▼ 1 b) Suppose that the growth rate is replaced by its average value 10 Determine the doubling time t in this case.

Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy (0.4 + sin t) dt || 4 NOTE: Round your answers to two decimal places. a) If y(0) 1, find (or estimate) the time T at which the population || has doubled. Choose other initial conditions and determine whether the doubling time ↑ depends on the initial population. The doubling time is 7 = The doubling time Choos depend on the initial population one ▼ 1 b) Suppose that the growth rate is replaced by its average value 10 Determine the doubling time t in this case.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need answers for a, b & c

Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy (0.4 + sin t) dt 4 NOTE: Round your answers to two decimal places. a) If y(0) = 1, find (or estimate) the time T at which the population has doubled. Choose other initial conditions and determine whether the doubling time t depends on the initial population. The doubling time is T = The doubling time Choose one depend on the initial population. 1 b) Suppose that the growth rate is replaced by its average value 10 Determine the doubling time T in this case. In this case, ↑ =
Transcribed Image Text:Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy (0.4 + sin t) dt 4 NOTE: Round your answers to two decimal places. a) If y(0) = 1, find (or estimate) the time T at which the population has doubled. Choose other initial conditions and determine whether the doubling time t depends on the initial population. The doubling time is T = The doubling time Choose one depend on the initial population. 1 b) Suppose that the growth rate is replaced by its average value 10 Determine the doubling time T in this case. In this case, ↑ =
c) Suppose that the term sin t in the differential equation is replaced by sin(2nt); that is, the variation in the growth rate has a substantially higher frequency. What effect does this have on the doubling time T ? In this case, ↑ =
Transcribed Image Text:c) Suppose that the term sin t in the differential equation is replaced by sin(2nt); that is, the variation in the growth rate has a substantially higher frequency. What effect does this have on the doubling time T ? In this case, ↑ =
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