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Consider the slight modification to the exponential growth equation given by dP dt kpl+c с where k> 0 and e > 0. Recall that if e = 0, the resulting linear equation has solution P(t) = P(0)et where the population, P(t), exhibits unbounded growth over the infinite time interval [0,00), that is, P(t) → ∞o as t→ ∞o. (a) Suppose for c = 0.01 the nonlinear differential equation P' = kp1.01 models the population of small animals where time, t, is measured in months. Find the solution to this nonlinear differential equation if the initial number of animals is 10 and it is known that the population doubles in the first 5 months. (b) What is the population after 50 months? 100 months? (c) The nonlinear differential equation in part (a) is called a doomsday equation because the population will grow without bound over a finite time interval [0, to). This means that P(t) → ∞o as t→ tō . Find to-

Consider the slight modification to the exponential growth equation given by dP dt kpl+c с where k> 0 and e > 0. Recall that if e = 0, the resulting linear equation has solution P(t) = P(0)et where the population, P(t), exhibits unbounded growth over the infinite time interval [0,00), that is, P(t) → ∞o as t→ ∞o. (a) Suppose for c = 0.01 the nonlinear differential equation P' = kp1.01 models the population of small animals where time, t, is measured in months. Find the solution to this nonlinear differential equation if the initial number of animals is 10 and it is known that the population doubles in the first 5 months. (b) What is the population after 50 months? 100 months? (c) The nonlinear differential equation in part (a) is called a doomsday equation because the population will grow without bound over a finite time interval [0, to). This means that P(t) → ∞o as t→ tō . Find to-

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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6. Consider the slight modification to the exponential growth equation given by dP dt kpl+c where k> 0 and e > 0. Recall that if c = 0, the resulting linear equation has solution P(t) = P(0)ekt where the population, P(t), exhibits unbounded growth over the infinite time interval [0, ∞o), that is, P(t) → ∞o as t→∞o. (a) Suppose for c = 0.01 the nonlinear differential equation P' = kp1.01 models the population of small animals where time, t, is measured in months. Find the solution to this nonlinear differential equation if the initial number of animals is 10 and it is known that the population doubles in the first 5 months. (b) What is the population after 50 months? 100 months? (c) The nonlinear differential equation in part (a) is called a doomsday equation because the population will grow without bound over a finite time interval [0, to). This means that P(t) → ∞o as t → to. Find to.
Transcribed Image Text:6. Consider the slight modification to the exponential growth equation given by dP dt kpl+c where k> 0 and e > 0. Recall that if c = 0, the resulting linear equation has solution P(t) = P(0)ekt where the population, P(t), exhibits unbounded growth over the infinite time interval [0, ∞o), that is, P(t) → ∞o as t→∞o. (a) Suppose for c = 0.01 the nonlinear differential equation P' = kp1.01 models the population of small animals where time, t, is measured in months. Find the solution to this nonlinear differential equation if the initial number of animals is 10 and it is known that the population doubles in the first 5 months. (b) What is the population after 50 months? 100 months? (c) The nonlinear differential equation in part (a) is called a doomsday equation because the population will grow without bound over a finite time interval [0, to). This means that P(t) → ∞o as t → to. Find to.
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