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?
Answers
Steve
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
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