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On the first day it was posted online, a music video got 310 views. The number of views that the video got each day increased by
20% per day. How many total views did the video get over the course of the first 6 days, to the nearest whole number?
Answer:

On the first day it was posted online, a music video got $310$ views. The number of views that the video got each day increased by $20 \%$ per day. How many total views did the video get over the course of the first $6$ days, to the nearest whole number? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q. On the first day it was posted online, a music video got

310

views. The number of views that the video got each day increased by

20 \%

per day. How many total views did the video get over the course of the first

6

days, to the nearest whole number?

\newline

Answer:

Determine initial views and rate: Determine the initial number of views and the daily increase rate. $\newline$ The initial number of views $V_0$ is $310$ , and the daily increase rate $r$ is $20\%$ .
Convert rate to decimal: Convert the daily increase rate to a decimal. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $r = 20\% = \frac{20}{100} = 0.20$
Calculate views for each day: Calculate the number of views for each day using the formula for exponential growth: $V = V_0 \times (1 + r)^n$ , where $V$ is the number of views, $V_0$ is the initial number of views, $r$ is the daily increase rate, and $n$ is the number of days. $\newline$ Day $1$ : $V = 310 \times (1 + 0.20)^1 = 310 \times 1.20 = 372$ $\newline$ Day $2$ : $V = 310 \times (1 + 0.20)^2 = 310 \times 1.44 = 446.4$ $\newline$ Day $3$ : $V = 310 \times (1 + 0.20)^3 = 310 \times 1.728 = 535.68$ $\newline$ Day $4$ : $V = 310 \times (1 + 0.20)^4 = 310 \times 2.0736 = 642.816$ $\newline$ Day $5$ : $V = 310 \times (1 + 0.20)^5 = 310 \times 2.48832 = 771.3792$ $\newline$ Day $6$ : $V$ $0$
Sum total views: Sum the total views from Day $1$ to Day $6$ . $\newline$ Total views = $\text{Day 1} + \text{Day 2} + \text{Day 3} + \text{Day 4} + \text{Day 5} + \text{Day 6}$ $\newline$ Total views = $372 + 446.4 + 535.68 + 642.816 + 771.3792 + 925.57504$ $\newline$ Total views = $3693.85024$
Round total views: Round the total views to the nearest whole number. $\newline$ Total views $\approx 3694$ (rounded to the nearest whole number)

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