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?

Question

paxpolaris · Answer

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

paxpolaris · Answer

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

zzr0ck3r · Answer

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

paxpolaris · Answer

rate of change of population = birth rate - death rate

you are given that birth rate “B(t)” is proportional to P(t)

zzr0ck3r · Answer

ahh alpha is praportional I see

zzr0ck3r · Answer

tyvm

paxpolaris · Answer

i'm getting $\large k=0.0101$

i hope u can take it from here.. i'm a bit rusty on differential equations

zzr0ck3r · Answer

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