Question

The function f(t)=100,000/1+5000e^(-t) represents the population of an endangered species bird t years after they were introduced to a non-threatening habitat.

a.In what year will there be 70,000 birds?

b.How many birds were intially introduced to the habitat?

c.How many birds are expected in the habitat eleven years after the introduction?

I'm thinking y=y0e^(-t)as the formula.
Looking for advice on set up of calculation, not necessarily answers to all.

Answer 1

a) So, 70000 = 10000/(1 + 5000e^(-t)
1+5000e^-t = 10/7
5000e^-t = 10/7 - 1 = 3/7
e^-t = 3/35000 = .000085714
ln both sides
-t = ln .000085714
-t = -9.36
t = 9.36 years

b) when t=0
f(0) = 100000(1+ e^0) = 100000/2 = 50000

c) plug in t=11, you do the button-pushing