Consider the differential equation OP - kpl +c where k > 0 and c2 0. In Section 3.1 we saw that in the case c = 0 the linear differential equation dP/dt = kP is a mathematical model of a population P(t) that exhibits unbounded growth over the infinite time interval [0, 0), that is, P(t) o as t - 00. See Example 1 in that section. (a) Suppose for c = 0.01 that the nonlinear differential equation dP = kp1.01, k > 0, is a mathematical model for a population of small animals, where time t is measured in months. Solve the differential equation subject to the initial condition P(0) = 10 and the fact that the animal population has doubled in 10 months. (Round the coefficient of t to six decimal places.) P(t) = (b) The differential equation in part (a) is called a doomsday equation because the population P(t) exhibits unbounded growth over a finite time interval (0, T), that is, there is some time T such that P(t) - o as t-T. Find T. (Round your answer to the nearest month.) T = months (c) From part (a), what P(90)? P(180)? (Round your answers to the nearest whole number.) P(90) = P(180) =
Consider the differential equation OP - kpl +c where k > 0 and c2 0. In Section 3.1 we saw that in the case c = 0 the linear differential equation dP/dt = kP is a mathematical model of a population P(t) that exhibits unbounded growth over the infinite time interval [0, 0), that is, P(t) o as t - 00. See Example 1 in that section. (a) Suppose for c = 0.01 that the nonlinear differential equation dP = kp1.01, k > 0, is a mathematical model for a population of small animals, where time t is measured in months. Solve the differential equation subject to the initial condition P(0) = 10 and the fact that the animal population has doubled in 10 months. (Round the coefficient of t to six decimal places.) P(t) = (b) The differential equation in part (a) is called a doomsday equation because the population P(t) exhibits unbounded growth over a finite time interval (0, T), that is, there is some time T such that P(t) - o as t-T. Find T. (Round your answer to the nearest month.) T = months (c) From part (a), what P(90)? P(180)? (Round your answers to the nearest whole number.) P(90) = P(180) =
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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