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As part of a laboratory experiment, the ...

As part of a laboratory experiment, the number of times a light id flashed on a certain culture of bacteria is reduced 20 percent each day. If the light flashed 704 times on the fourth day of the experiment, then the number of times it flashed on the first day is closest to

A

880

B

`1,217`

C

`1,267`

D

`1,375`

Text Solution

Verified by Experts

The correct Answer is:
D
The key insight here is to notice that when 20% of the flashes are removed, 80% remain. Call the number of flashes on the first day F. Then the number of flashes on the second day is `F - (1)/(5)F=(4)/(5)F`. On the third day, the number is 80% or `(4)/(5)` of `(4)/(5)` of F - which you can express more simply as `((4)/(5))^(2)F`. Similarly, on the fourth day, the number of flashes is `((4)/(5))^(3)F`. You're given that the number, of flashes on the fourth day is 704, so `704=((4)/(5))^(3)F=(4^(3))/(5^(3))F=(64)/(125)F=(64F)/(125)`. If `704=(64F)/(125)`, then `F = 704((125)/(64))`. Use your calculator : `F = 1,375`.
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