Problem of the Day


On Sunday evening, Eric posts a video to the internet that is viewed 15 times by the end of the day. On Monday, the number of views doubles. The number of views continues to double on every weekday, Monday through Friday, and then triples on each day of the weekend, Saturday and Sunday. If this pattern continues, with his number of views doubling on weekdays and tripling on weekend days, how many views will his video have at the end of the 17th full day?

A. 2^{13}\cdot3^5\cdot5
B. 15+13\cdot2+ 4\cdot3
C. 15\cdot2^{14}\cdot3^3
D. 2^{13}\cdot3^4
E. 15\cdot6^{17}

Reveal Answer

Answer

[latexpage]

A. $2^{13}\cdot3^5\cdot5$

See the Solution

Solution

[latexpage]

He starts with 15 views on Sunday. Every day that his view count doubles, the count is multiplied by 2. Every time it triples, the count is multiplied by 3. In the 17 full days after he posts the video there are 13 weekdays and 4 weekend days. Hence, the total number of views would be $15\cdot2^{13}\cdot3^4$. Writing 15 as $3\cdot5$ gives us $3\cdot5\cdot2^{13}\cdot3^4$. Simplifying this with exponent laws and writing the bases in ascending order gives the form of the final answer, $2^{13}\cdot3^5\cdot5$.


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