The population of birds vary as \(A=A_0 e^{kt}\)

Given that population of brds fell from 1400 to 1000,we are asked how much time it will ake forthe population to fall below 100 when t=5

we can write the following equation

\(1400=1000e^{5k}\)

\(k=(1.4)/(5)\)

we need to find x,such that \((1400)/(100)=(e^x k)\)

\(14=(e^{xk})\)

in (14)=kx

\(x=(5 \in (14))/(\in(1.4)) \approx 39\) years

It will take 39 years for the population f birds to fall below 100