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If 35% of the acreage of a national forest was destroyed in a wildfire

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Bunuel
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If 35% of the acreage of a national forest was destroyed in a wildfire [#permalink] New post   13 Jul 2021, 08:30
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If 35% of the acreage of a national forest was destroyed in a wildfire, and the remainder regenerates at a rate of 10% a year, after how many years, assuming no further losses, will the forest exceed its original acreage?

(A) 10
(B) 8
(C) 5
(D) 4
(E) 3
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C
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If 35% of the acreage of a national forest was destroyed in a wildfire [#permalink] New post   13 Jul 2021, 09:37
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Bunuel wrote:
If 35% of the acreage of a national forest was destroyed in a wildfire, and the remainder regenerates at a rate of 10% a year, after how many years, assuming no further losses, will the forest exceed its original acreage?

(A) 10
(B) 8
(C) 5
(D) 4
(E) 3


We start at 65% and regen 10% of the current 65% per year. If we set up an equation, we have \(65\%*(1.1)^x = 100\%\). Yet the faster and easier way is to count year by year, the first year we regen 6.5% and reach 71.5%.

For the 2nd year, we regen 7.15% and reach 78.65%. We can see we roughly gain 8% per year from now on and we are missing 21.35%, so after 3 years from then, we will exceed 100%. In total that is 5 years.

Ans: C
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Re: If 35% of the acreage of a national forest was destroyed in a wildfire [#permalink] New post   16 Jul 2021, 07:49
Assuming the acreage to be 100
65*1.1^n=100
1.1^n=1.53
Hence, n= approx 5 years
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Re: If 35% of the acreage of a national forest was destroyed in a wildfire [#permalink] New post   10 Jan 2022, 10:52
65% (1.1)^n > 100%

=> (1.1)^n >1.5

n=5.
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Re: If 35% of the acreage of a national forest was destroyed in a wildfire [#permalink] New post   04 Dec 2022, 08:31
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Instead of forest, think it as money…we had 100 rs.. it reduced 35% to become 65, now it grows by 6.5 rs every year… just divide 35/6.5= 5.3 something … 5 approx
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Re: If 35% of the acreage of a national forest was destroyed in a wildfire [#permalink] New post   17 Mar 2024, 09:20
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Re: If 35% of the acreage of a national forest was destroyed in a wildfire [#permalink]
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