Question

On the first day it was posted online, a music video got 580 views. The number ofviews that the video got each day increased by 30% per day. How many total viewsdid the video get over the course of the first 25 days, to the nearest whole number?

Answer 1

By definition, if a quantity grows by a fixed percent at regular intervals, the pattern can be depicted by this function:

`\begin{gathered} y=a(1+r)^x\Rightarrow\text{ Exponential growth} \\ \text{ Where a is the initial value} \\ r\text{ is the growth rate, represented as a percentage and expressed as a decimal} \\ x\text{ is the number of time intervals that have passed} \end{gathered}`

So, in this case, you have

`\begin{gathered} a=580 \\ r=0.3\text{ because 30\%}=(30)/(100)=0.3 \\ x=25\text{ because the time is the first 25 days} \end{gathered}`
`\begin{gathered} y=a(1+r)^x \\ y=580(1+0.3)^(25) \\ y=580(1.3)^(25) \\ y=580\cdot705.64 \\ y=409,271.78 \\ \text{ Rounding to the nearest whole number} \\ y\approx409,272 \end{gathered}`

Therefore, the video earned 409,272 total views over the course of the first 25 days, rounded to the nearest whole number.