Question

A population grows exponentially. If the population is 0.5sqrt(e) at one year and 0.5e at two years, what is it at 4 years?

Answer 1

we know that

p = ae^kt

using the known values,

√e/2 = ae^k
e/2 = ae^2k

divide to get

(e/2) / (√e/2) = e^k
√e = e^k
so, k = 1/2

now, we see that
√e/2 = ae^(1/2)
so a = 1/2

p(t) = 1/2 e^(t/2)

p(4) = 1/2 e^2