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# solve population growth

Under ideal conditions, a population of rabbits has an exponential growth rate of 11.7% per day. Consider an initial population of 100 rabbits.
(a) Find the exponential growth function
(b) What will the population be after one week? After 2 weeks?
(c) Find the doubling time.

P = P0ekt

In this case

(a) P = (100)e(0.117)(t)

(b) P = (100)e(0.117)(7 days)

P = 226.8

(c) 200 = (100)e(0.117)t

e(0.117)(t) = 2

(0.117)(t) = ln(2)

t = 5.92 days

Start by noting the variables:
A(t)=A*ekt
Where k is the growth rate (in decimals) and t is the time (in days)  A is the original amount or initial population, and A(t) represents the population at time t.
So,
The growth function is:
A(t)=100e.117t

The population at time t=1 week (7 days) and t=2 weeks (14 days)
is:
For 1 week, t=7
A(7)=100e.117*7=226.8 or 226
For 2 weeks, t=14
A(14)=100e.117*14=514.4 or 514
Finally the doubling time is:

200=100e.117*t
So 2=e.117t
take the ln of both sides:
ln(2)=.117t
t=ln(2)/.117= 5.92 days, or 6 days.