Consider a population of field mice who inhabit a certain rural area. We assume

Question

Consider a population of field mice who inhabit a certain rural area. We assume that mouse population increases at 50 % rate proportional to the current population per month. Furthermore several owls live in the same neighborhood and they kill 450 mice per month. The model explain the situation is the following. ????????=0.5???450
In here, ?? denotes the population of mice as months.
a) Find the time at which the population becomes extinct if ??(0)=850.
b) Find the time of extinction if ??(0)=??0, where 0<??0<900.
c) Find the initial population ??0 if the population is to become extinct in 1 year.

Explanation / Answer

dp/dt = 0.5p -450

2dp/(p -900) = dt

2ln(p-900)= t+c

p(t) = 900 + ket/2

p(0) = 850 = 900+k

=> k = -50

p(t) = 900 - 50et/2

(a) 900 - 50et/2 = 0 => t = 2ln(900/50) = 5.78 months

(b) p(0) = 0 => p0 = 900 + k => k = p0 - 900

p(t) = 900 +(po - 900)et/2

p(t) = 0 => t = 2ln(900/(900-po))

(c) t = 12 months = 2ln(900/900-po)

=> e6 = 900/900 - p0

=> 900 - p0 = 900e-6

=> p0 = 900 - 900e-6 = 898 (rounded off)

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.