Algebra

[BTGmoderatorRO]

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

[EconomistGMATTutor]

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.

[Scott@TargetTestPrep]

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

Since the size of the bacteria doubles each day and it takes 30 days to fill the laboratory dish with bacteria, it must be true that it took 29 days to fill half of the dish with bacteria (since the following day, the 30th day, the size of the bacteria will double and fill the entire dish).

Answer: D

[Brent@GMATPrepNow]

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

KEY INFO: The size of the bacteria doubles each day
So, we can write: (size of bacteria on Day 29)(2) = (size of bacteria on Day 30)

GIVEN: On Day 30, the dish is at 100% capacity
So, we can write: (size of bacteria on Day 29)(2) = (100% capacity)
Divide both sides by 2 to get: (size of bacteria on Day 29) = (100% capacity)/2
Simplify: (size of bacteria on Day 29) = 50% capacity

So, on Day 29, the dish was HALF (aka 50%) full.

Answer: D

Cheers,
Brent