Respuesta :
Using an exponential function, it is found that the video got 8,314 total views over the course of the first 12 days.
What is an exponential function?
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
- A(0) is the initial value.
- r is the growtn rate, as a decimal.
On the first day it was posted online, a music video got 250 views, and the number increased by 16% a day, hence the A(0) = 250, r = 0.16, and the equation is given by:
[tex]A(t) = 250(1.16)^t[/tex]
The total amount over the first 12 days is given by:
[tex]T = \int_{0}^{12} A(t) dt[/tex]
[tex]T = \int_{0}^{12} 250(1.16)^t dt[/tex]
[tex]T = 250\frac{(1.16)^t}{\ln{1.16}}|_{t = 0}^{t = 12}[/tex]
Applying the Fundamental Theorem of Calculus:
[tex]T = 250\frac{(1.16)^{12}}{\ln{1.16}} - 250\frac{(1.16)^0}{\ln{1.16}}[/tex]
T = 8314.
The video got 8,314 total views over the course of the first 12 days.
More can be learned about exponential functions at https://brainly.com/question/25537936
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