Question

aftera particularly harsh winter, the regrowth of a population of rabbit in an area is given by p(t)=500/1+e^-t. whare t is the time in years . determine the rate of growth in population after 3years. please need help. thanks.

Answer 1

The *average* rate of growth or true rate of growth?

Answer 2

Rate of growth. please.

Answer 3

Er...? Is this for calculus or what subject? (A better question)

Answer 4

calculus.....

Answer 5

All right, so we differentiate using such:
\[
\frac{d}{dt}\left(\frac{500}{1-e^{-t}}\right)=\frac{d}{dt}(500)(1-e^{-t})^{-1}
\]Using the product rule:
\[
\frac{d}{dt}(500)(1-e^{-t})^{-1}=0\cdot(1-e^{-t})^{-1}+(500)\left(\frac{d}{dt}(1-e^{-t})^{-1}\right)
\]Using the chain rule gives us:
\[
500e^{-t}(e^{-t}+1)^{-2}=\frac{500e^{-t}}{(e^{-t}+1)^2}
\]We simply plug in t=3 and et voilá.