There are 64000 subscribers to an online fashion magazine. Due to competition from a new magazine, the number C(t) of subscribers is expected to decrease at the rate of C'(t)= -600t1/3

Question

Subscribers per month, where t is the time in months where the new magazine began publication. How long will it take until the number of subscribers to the online fashion magazine drops to 46000?

Answer 1

We get C(t) by integrating derivative: C(t) = ∫(- 600t^1/3)dt = - 600t^4/3 · 3/4 + D = - 450t^4/3+ D, wher D is arbitrary constant. To get D we use condtion C(0) = 64000. We have now: D = 64000 and C(t) = 64000 - 450t^4/3.

Now to get needed to decrease number of subscribers to 46000 we get equation:

46000 = 64000 - 450t^4/3, 450t^4/3 = 64000 - 46000, 450t^4/3 = 18000, t^4/3 = 40, t = 40^3/4 = 15.9 month