population of rabbits is given by p(t)=500/1+e^-t determine the rate of growth after 3 years

Question

population of rabbits is given by p(t)=500/1+e^-t     determine the rate of growth after 3 years

amistre64 · Answer

rate of growth sounds like its asking for a derivative at 3 years

anonymous · Answer

why is that e in the function. i dont know how to get the answer because of the e

amistre64 · Answer

the "e" represents a transmutational number ... transmigratory? trans-something ...

its a number that comes up alot in natural phenomenae

amistre64 · Answer

p(t)=500/(1+e^-t)

p(t) = 500 (1+e^-t)^-1

p'(t) = 500 -(1+e^-t)^-2 (-e^-t)
       = (-500 e^-t)/(1+e^-t)^2

p'(3) = (-500 e^-3)/(1+e^-3)^2
        =abt -22.588....

this tells us the growth rate is declining by about 22.588 after 4 years

anonymous · Answer

but what is the valu of e?

amistre64 · Answer

it has a "value" attributed to it just like "pi" does.

e = 2.71828182845905....... if i recall it correctly