Answer to Question #209469 in Algebra for Elias

Question

In a farm, there initially were 10 rabbits. After three months, there are already 20 rabbits. Assuming that the growth is exponential and no rabbit dies in the process, at what time will there be 100 rabbits?

Answer 1

$N(t)=ae^{bt}$ .

$N(0)=10\to a=10.$

$N(3)=20\to 10e^{3b}=20\to b=\frac{ln2}{3}=0.2310.$

$100=10e^{0.2310t}\to t=\frac{ln10}{0.2310}=10\;months.$