Answer:
Step-by-step 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.
