Question

On a day, a video was posted online, 5 people watched the video. The next day the number of viewers had doubled. This tend continues each day. Write an equation modeling the views, v, as a function of time.

On which day will 640 people see the video? Explain if you can.

Answer 1

• v(t) = 5·2^(t-1)
• day 8

Explanation:

The number of viewers is a geometric sequence with 5 viewers on day 1 and a common ratio of 2. The general term will be ...

v(t) = 5·2^(t-1) . . . . . . viewers on day t

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We want to find t for v(t) = 640.

640 = 5·2^(t-1) . . . . . use v(t)=640

128 = 2^(t-1) . . . . . . . divide by 5

2^7 = 2^(t -1) . . . . . . . recognize 128 = 2^7

7 = t -1 . . . . . . . . . . . . equate exponents of 2

8 = t . . . . . . . add 1

There will be 640 viewers on day 8.

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Comment on the equation and solution

The problem statement doesn't tell you how time is counted. If you treat the problem as one requiring an exponential function, you can also write the equation as ...

v(t) = 5·2^t

where t is the number of days after the first day. Then the solution will be ...

640 = 5·2^7 ⇒ t = 7 . . . . days after the first day

7 days after the first day is the same as Day 8, if the first day is Day 1.