SOLUTION: Bacteria in a dish double the area they cover everyday. If the dish is fully covered after 25 days, on what day was 1/2 of it covered?

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Question 1010633: Bacteria in a dish double the area they cover everyday. If the dish is fully covered after 25 days, on what day was 1/2 of it covered?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
On the day 24-th.

It is clear without any explanations.

    (It is old joke problem).





Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=p%28b%29%5Ex
The dish is in some area unit.
y is how much of some area unit same unit as p.
p is initial amount of area.
x is days time
b is a factor like a rate.

Bacteria in a dish double the area they cover everyday.
2=1%2Ab%5E1
b=2
highlight_green%28y=p%2A2%5Ex%29

the dish is fully covered after 25 days
y is the one whole dish. y=1 when x=25.
1=p%2A2%5E25
p=1%2F2%5E25 a very small amount of the dish.


The model may be highlight_green%28y=%281%2F2%5E25%292%5Ex%29.

The question is, what is x, when y=1/2 ?
log%28%28y%29%29=log%28%282%5E-25%29%29%2Bx%2Alog%28%282%29%29
log%28%28y%29%29=-25%2Alog%28%282%29%29%2Bx%2Alog%28%282%29%29
log%28%28y%29%29%2B25%2Alog%28%282%29%29=x%2Alog%28%282%29%29
%28log%28%281%2F2%29%29%2B25%2Alog%28%282%29%29%29%2Flog%28%282%29%29=x
highlight%28x=log%28%281%2F2%29%29%2Flog%28%282%29%29%2B25%29

Choose the base you want for the logarithms: Natural or Common.
Compute x.


(Day 24)