(a) Find the exponential growth function

(b) What will the population be after one week? After 2 weeks?

(c) Find the doubling time.

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.

(a) Find the exponential growth function

(b) What will the population be after one week? After 2 weeks?

(c) Find the doubling time.

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P = P_{0}e^{kt}

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*e^{kt}

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.

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