Question

Suppose that a fish population t days from now can be modeled by an exponential function P(t) = Ae^kt". Suppose that the fish population doubled in 90 days. By how much will the fish have multiplied from its initial number after 120 days?

Answer 1

$P(0) = Ae^{k*0} = A$

$P(90) = Ae^{90k}$

$2P(0) = P(90) \to 2A = Ae^{90k} \to 90k = ln2 \to k ={\frac {ln2} {90}}$

$P(120) = Ae^{120k}$

${\frac {P(120)} {P(0)}}= e^{120k} = e^{{\frac 4 3}*ln2} = (e^{ln2})^{{\frac 4 3}} = 2^{\frac 4 3}$

After 120 days population of fish will be multiplied be $2^{\frac 4 3}$, or approximately by 2.83