Question

Nora uploaded a funny video on her website, which rapidly gains views over time. The following function gives the number of views ttt days after Nora uploaded the video: V(t)=100⋅e0.4t What is the instantaneous rate of change of the number of views 444 days after the video was uploaded?

Answer 1

Every day, the number of views grows by a factor of 1.53.

Explanation:

Answer 2

about 198.1

Explanation:

The instantaneous rate of change is given by the derivative:

V'(t) = 100·e^(0.4t)(0.4)

V'(t) = 40·e^(0.4t)

So V'(4) is ...

V'(4) = 40·e^1.6 ≈ 198.1213

The instantaneous rate of change of views at day 4 is 198.1 views per day.