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

Question

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

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

TestPrepUnlimited · Answer

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

Nitisha03 · Answer

Assuming the acreage to be 100
65*1.1^n=100
1.1^n=1.53
Hence, n= approx 5 years

Arvind123 · Answer

65% (1.1)^n > 100%

=> (1.1)^n >1.5

n=5.

A2D2 · Answer

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

luisdicampo · Answer

Deconstructing the Question

35% of the forest is destroyed, so  65% remains . 
The remaining forest grows at  10% per year . 
We need the number of years until the forest exceeds its original size.

Step-by-step

Forest size after n years:

0.65(1.1)^n

We want:

0.65(1.1)^n > 1

So:

(1.1)^n > \frac{1}{0.65}

\frac{1}{0.65} \approx 1.538

Compute powers:

(1.1)^2 = 1.21

(1.1)^3 = 1.331

(1.1)^4 \approx 1.464

(1.1)^5 \approx 1.61

Since  1.61 > 1.538 , the forest exceeds the original size after 5 years.

Answer: 5

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

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

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