Eitan posted a video on the internet which only received approximately $100$ views per day for the first $365$ days after it was posted. However, on the $366^{\text {th }}$ day, Eitan's video began to receive a greater following: the total number of views grew at a rate of $25 \%$ per day. Compared to the number of views Eitan's video received in the first $365$ days, how many more views did his video receive in the $7$ -day period after the first $365$ days? $\newline$ Choose $1$ answer: $\newline$ (A) $36$ , $500$ $\newline$ (B) $101$ , $000$ $\newline$ (C) $138$ , $000$ $\newline$ (D) $174$ , $000$

Full solution

Q. Eitan posted a video on the internet which only received approximately

100

views per day for the first

365

days after it was posted. However, on the

366^{\text {th }}

day, Eitan's video began to receive a greater following: the total number of views grew at a rate of

25 \%

per day. Compared to the number of views Eitan's video received in the first

365

days, how many more views did his video receive in the

7

-day period after the first

365

days?

\newline

Choose

1

answer:

\newline

(A)

36

500

\newline

(B)

101

000

\newline

(C)

138

000

\newline

(D)

174

000

Calculate total views: Calculate the total views for the first $365$ days. $100$ views/day $*$ $365$ days = $36,500$ views
Determine $366$ th day views: Determine the number of views on the $366^{th}$ day. $\newline$ $25\%$ increase from $100$ views = $100$ views + $(\frac{25}{100} \times 100$ views) = $125$ views
Calculate total views next $7$ days: Calculate the total views for the next $7$ days using the daily growth rate. $\newline$ Day $1$ : $125$ views $\newline$ Day $2$ : $125$ views $\times 1.25 = 156.25$ views $\newline$ Day $3$ : $156.25$ views $\times 1.25 = 195.3125$ views $\newline$ Day $4$ : $195.3125$ views $\times 1.25 = 244.140625$ views $\newline$ Day $5$ : $244.140625$ views $\times 1.25 = 305.17578125$ views $\newline$ Day $6$ : $305.17578125$ views $125$ $0$ views $\newline$ Day $7$ : $125$ $1$ views $125$ $2$ views
Add total views $7$ -day period: Add up the total views for the $7$ -day period after the first $365$ days. $\newline$ Total views = $125 + 156.25 + 195.3125 + 244.140625 + 305.17578125 + 381.4697265625 + 476.837158203125$ $\newline$ Total views = $1884.185541015625$ views
Compare total views: Compare the total views in the $7$ -day period to the first $365$ days. $\newline$ Difference in views $= 1884.185541015625$ views $- 36,500$ views