Answer to Question #271570 in Differential Equations for Hania

Question

Suppose a population of insects according to the law of exponential growth/decay. There were 130 insects after the third day of the experiment and 380 insects after the 7th day. Approximately how many insects were in the original population?

Answer 1

130 insects after 3 days

380 insects after 7 days

$y=Ae^{Bt}$

$130=Ae^{3B}$ ..........(i)

$380=Ae^{7B}$ ..........(ii)

Dividing equation (ii) by (i) we get;

$\frac{380}{130}=\frac{Ae^{7B}}{Ae^{3B}}$

$\frac{38}{13}=\frac{e^{7B}}{e^{3B}}=e^{7B}*e^{-3B}=e^{4B}$

$ln(\frac{38}{13})={4B}$

B=0.2681

Replace this in equation (i) to get A

$130=Ae^{3B}$

$130=Ae^{3*0.2681}=Ae^{0.80}$

130=2.226A

A=58.4

Initial insect population at t=0

$y=Ae^{B*0}$

$\therefore y=A$

y=58.4 insects

$\approx 59$ insects