Question

B(t)=4*e^0.8t, How many hours will it take for the population to grow to 400?

A colony of bacteria is growing exponentially according to the function below, where t is in hours. How many hours will it take for the population to grow to 400

Answer 1

Given: "B(t)=4*e^0.8t, How many hours will it take for the population to grow to 400?" Set B(t) = 400. Then:

400=4*e^(0.8t), or

100 = e^(0.8t)

Take the natural log of both sides, obtaining
ln 100
ln 100 = 0.8t. Then t = ----------- = 5.76 hours.
0.8