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Algebra

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Algebra

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It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill one half of dish?

A) 10 days
B) 15 days
C) 24 days
D) 29 days
E) 29.5 days
OA is d
It's a simple problem here but I am struggling to express what happens here algebraically. Please help me Confused Confused

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GMAT/MBA Expert

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Hello Roland. I hope I can clarify it to you.

You can establish a function that represents the growth of bacteria as follows:
$$f\left(t\right)=2^t$$
where t is the number of days.

If it takes 30 days to fill a laboratory dish it implies that the capacity of the laboratory dish is $$f\left(30\right)=2^{30}.$$

The half of the capacity is $$\frac{2^{30}}{2}=2^{29}.$$

Note that this final result is equal to f(29).

So, the half of the laboratory dish is filled after 29 days,

The correct answer is D.

I'm available if you'd like any follow up.

Regards.

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