Question

A population of squirrels living in a forest with a carrying capacity of 2600.(assume logistics growth with constant k=0.9yr)

(a)find a formula for the squirrels population p(t) assuming an initial population of 650 squirrels.

(b)how long will it take for the squirrels population to double?

Answer 1

(a) p(t)=(pke^(rt))/((k-p)+pe^(rt))

Where p -is the initial population

            k -carrying capacity

            r -growth rate

So , we get

      (650*2600e^(0.9t))/((2600-650)+650e^(0.9t))

=(2600e^(0.9t))/(3+e^(0.9t))

 

(b) t=1/rln(k-p)/p

     =1/0.9ln(2600-650)/650

     =1/0.9ln3

     =1.2207

(a)=(2600e^(0.9t))/(3+e^(0.9t))

(b)=1.2207