A given field mouse population satisfies the differential equation dp/dt=.4p-450 where p is the number of mice and t is the time in months. (a) Find the time at which the population becomes extinct if p(0)=1075
Round your answer to two decimal places in months.
(b) Find the initial population Po if the population is to become extinct in 1 year.
Round your answer to the nearest integer.
Po= mice

a) 7.78 months

b) 1116

Step-by-step explanation:

Given -

Integrating the above equation with respect to time, we get -

let us define new variable x

substituting these values in above integral equation, we get -

at t = 0, P (0) = 1075, using this condition, we get -

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1