Question

Consider an animal population P(t) with constant death rate s = 0.02 ( deaths per animal per month) and with birth rate B proportional to P. Suppose that P(0) = 200 and P`(0) = 2. When is P = 1000?

Answer 1

\[\large P'(t)=B(t)-s\]
and, \(\large \because B(t) \propto P(t) \implies B(t) = k \cdot P(t) \)
for some constant k

Answer 2

solve for k using \[\large P'(0)= k \cdot P(0)-0.02\]

Answer 3

what is the B(t) alpha P(t)?

Answer 4

rate of change of population = birth rate - death rate

you are given that birth rate “B(t)” is proportional to P(t)

Answer 5

ahh alpha is praportional I see

Answer 6

tyvm

Answer 7

i'm getting \(\large k=0.0101\)

i hope u can take it from here.. i'm a bit rusty on differential equations

Answer 8

yeah for susre, just wanted to know what it was saying:)