help solve this calculus problem

Question

A yeast culture is growing at the rate of �,

W`(t)= 0.2e^0.1t grams per hour. If the

starting culture weighs 4 grams. What will be the weight of the culture W(t) after

t hours? After 8 hours?

Answer 1

This is a differential equation problem.

W'(t) = 0.2e^0.1t

dW/dt = 0.2e^0.1t

dw = 0.2e^0.1t dt

Now you can integrate both.

W(t) = 0.2 [e^0.1t/0.1] + C

W(t) = 2 [e^0.1t] + C

Now we know W(0) = 4

W(0) = 2e⁰+C

C = 4-2

C = 2

After t hours, W(t) = 2 e^0.1t + 2

After 8 hours, W(8) = 2e^0.1*8+2 = 6.45 gram

I hope this helps...