A video posted on the internet is becoming very popular, and the total number of views is increasing by 30% every hour. If the video currently has 11,882 views, how many views will... A video posted on the internet is becoming very popular, and the total number of views is increasing by 30% every hour. If the video currently has 11,882 views, how many views will it have in 3 hours? If necessary, round your answer to the nearest whole number.
Understand the Problem
The question describes a scenario where a video's views increase by 30% every hour. Given the initial number of views (11,882), we need to calculate the total number of views after 3 hours, rounding to the nearest whole number. This involves calculating compound growth.
Answer
26105
Answer for screen readers
26105
Steps to Solve
- Calculate the growth factor
Since the views increase by 30% each hour, the growth factor is $1 + 0.30 = 1.30$.
- Calculate the views after 3 hours
Use the formula for compound growth: $Final,views = Initial,views \times (growth,factor)^{number,of,hours}$. In this case, $Final,views = 11882 \times (1.30)^3$.
- Compute $(1.30)^3$
$(1.30)^3 = 1.30 \times 1.30 \times 1.30 = 2.197$
- Calculate final views
$Final,views = 11882 \times 2.197 = 26104.754$
- Round to the nearest whole number
Rounding $26104.754$ to the nearest whole number gives $26105$.
26105
More Information
The number of views increases significantly over the 3 hours, nearly doubling from the initial amount. The total number of views after 3 hours is 26105.
Tips
- Forgetting to add 1 to the percentage increase when calculating the growth factor.
- Rounding too early in the calculation, which can lead to a less accurate final result.
- Using a simple interest calculation instead of a compound interest calculation.
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