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Exponents and Powers

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by sarthak030920 » Fri Aug 07, 2020 10:57 am

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E

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The number of water lilies on a certain lake doubles every two days. If there is exactly one water lily on the lake, it takes 60 days for the lake to be fully covered with water lilies. In how many days will the lake be fully covered with lilies, if initially there were two water lilies on it?

(A) 15
(B) 28
(C) 30
(D) 58
(E) 59
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Re: Exponents and Powers

by Scott@TargetTestPrep » Tue Aug 18, 2020 10:29 am
sarthak030920 wrote: ↑
Fri Aug 07, 2020 10:57 am
 The number of water lilies on a certain lake doubles every two days. If there is exactly one water lily on the lake, it takes 60 days for the lake to be fully covered with water lilies. In how many days will the lake be fully covered with lilies, if initially there were two water lilies on it?

(A) 15
(B) 28
(C) 30
(D) 58
(E) 59
Solution:

Since 60 days is a “long” period of time in terms of doubling. Let’s say it only takes 6 days for the lake to be fully covered with water lilies. That is,

Day 0 = 1

Day 2 = 2

Day 4 = 4

Day 6 = 8

Now, if initially there are 2 water lilies in the lake, we have:

Day 0 = 2

Day 2 = 4

Day 4 = 8

We see that it takes 2 fewer days for the lake to be fully covered with water lilies had the initial number of lilies been 2. Therefore, it will take 58 days for the lake to be fully covered with water lilies if the initial number of lilies is 2.

Answer: D

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Re: Exponents and Powers

by shekki » Tue Aug 18, 2020 12:30 pm
Since the lilies doubles every two days, we can apply the formula of compound interest as
Number of lilies = 1 x (1+1)^n

Where n = number of times the lilies double. So in first case, n =60/2 = 30, hence total lilies = (1+1)^30 = 2^30

Now, since there are two lilies in the beginning, the formula becomes as :
Number of lilies = 2x(1+1)^n
Now from earlier we know that this equals to 2^30
Equating both, 2^30 = 2 x 2^n
Solving, n = 29
Hence total number of days = 2n = 58 (D)
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