Question

A scientist monitored the number of fish in a lake and found that the number of fish increased at a rate proportional to the number of fish present. At time t=0 years, there were 200 fish in the lake. At time t=2 years, there were 1000 fish in the lake. What will be the number of fish in the lake at time t=4 years?

Answer 1

Answer:

5000 fishes

Explanation:

Let the model of the number of fish be in the form of

$P = Ae^{kt}$

where t is the time (in year). So the rate of increasing would be proportional to the number of fishes presented in the lake

At t=0, P = 200

$200 = Ae^0$

$A = 200At t = 2, P = 1000[tex] 1000 = 200e^{2k}$

$e^{2k} = 1000 / 200 = 5$

$2k = ln5$

$k = ln5/2 = 0.805$

At t = 4,

$P = 200e^{0.805*4} = 200*25 = 5000$