Suppose you had 20 rabbits After six months the number of ra

Suppose you had 20 rabbits. After six months the number of rabbits had increased to 100. If the number of rabbits increased exponentially, then how many rabbits will you have at the end of one year? What does it mean to increase exponentially?

Solution

Twnty initially...

So, we have
A = Pe^(rt)

Using A = 20 when t = 0 :
20 = P * e^0
20 = P

So,
A = 20e^(rt)

And now when t = 6(mths), A = 100 :
100 = 20e^(6r)

5 = e^(6r)

ln(5) = 6r

r = 1/6 * ln(5)

r = ln(5^(1/6))

And now
A = 20e^(rt)

becomes

A = 20(5^(1/6))^t

So,

A = 20(5)^(t/6) where t = is in months

Now, plug in t = 12 for the end of yr :
A = 20(5)^(12/6)

A = 20(5^2)

A = 20*25

A = 500 ---> ANS