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Extended Answer Question 1 (i) Suppose a population of parasites is being introduced into an island at an increasing rate 1- et parasites/day and is being killed by pesticide at rate 1/day. Suppose the population of parasites, P(t), at time t (measured in days) follows the differential equation 1-e¹ - P. dP dt (a) If the initial parasite population P(0) 100, determine the population P(t) over time. (b) What is the asymptotic behaviour of P(t) as t→→ ∞o?

Extended Answer Question 1 (i) Suppose a population of parasites is being introduced into an island at an increasing rate 1- et parasites/day and is being killed by pesticide at rate 1/day. Suppose the population of parasites, P(t), at time t (measured in days) follows the differential equation 1-e¹ - P. dP dt (a) If the initial parasite population P(0) 100, determine the population P(t) over time. (b) What is the asymptotic behaviour of P(t) as t→→ ∞o?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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Extended Answer Question 1 (i) Suppose a population of parasites is being introduced into an island at an increasing rate 1- et parasites/day and is being killed by pesticide at rate 1/day. Suppose the population of parasites, P(t), at time t (measured in days) follows the differential equation 1-e¹ - P. dP dt (a) If the initial parasite population P(0) 100, determine the population P(t) over time. (b) What is the asymptotic behaviour of P(t) as t→→ ∞o?
Transcribed Image Text:Extended Answer Question 1 (i) Suppose a population of parasites is being introduced into an island at an increasing rate 1- et parasites/day and is being killed by pesticide at rate 1/day. Suppose the population of parasites, P(t), at time t (measured in days) follows the differential equation 1-e¹ - P. dP dt (a) If the initial parasite population P(0) 100, determine the population P(t) over time. (b) What is the asymptotic behaviour of P(t) as t→→ ∞o?
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