The general function P(t)= 640ekt is used to model a dying bird population, where Po = 640 is the initial population and t is time measured in days. Suppose the bird population was reduced to one quarter of its initial size after 9 days. How long will it take before there are only 40 birds left in the population? Simplify your answer as much as possible.

Question

PLease help and show all work Thank you!

Answer 1

I am positive that you meant:
P(t) = 640 e^(kt)
given: when t = 9, P(t) = 160
640 e^(9k) = 160
e^(9k) = .25
9k = ln .25
k = ln.25/9 = -.154033

640 e^( -.154033 t) = 40
e^(-.154033 t) = .0625
-.154033 t = ln .0625
t = ln .0625/-.154033 = 18 days

Answer 2

It took 9 days to shrink to 1/4 its size.

40/640 = 1/16 = 1/4 * 1/4

So, it will take another 9 days to do that again.