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exponential functions

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this isnt really related to programming, but it is to math of course, but this is driving me insane. i just cant figure this out. its probably something stupid im not doing. anyways the problem. A culture of bacteria double in number every 15 minutes. After 8 hours the number of bacteria in the culture is X. At this rate, how long will it take for the total population of bactera to reach 16X? the answer is 9 hours. all i know is that N(t) = N(0) * (M ^ (t/d)) where N(t) is the number at anytime. N(0) is number when t is 0, t is the time, M is the multiplier (2 in this question) and d is the period (15 minutes in this case) i just cant get this question. thanks in advance to anyone who can shed some light on this. note: this isnt a homework problem for marks or anything its just review for studying.

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You're reading into this too far...

Required Growth = 16X / X = 16
Since growth doubles, 16 = 2^x with x = 4.
4 * 15 minutes = 1 hour. 8 hours + 1 hour = 9 hours.

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Umm... I think you're over thinking this. At 8 hours the population is X. It doubles every 15 minutes.

So at 8:15 it's 2X
8:30 it's 4X
8:45 it's 8X
9:00 it's 16X.

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wow that's all i can say. usually over thinking is my problem in math, funny how i coudnt get this but solving all the somewhat complex stuff in my class is easy as pie. thanks for the help.

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