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question on percent

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question on percent

by [email protected] » Mon Oct 17, 2016 5:17 am
Request you to help me with the solution for the following, why would the interest be 1.1 here?

If 35% of the acreage of a national forest was destroyed in a wild fire, and the remainder regenerates at a rate of 10% a year, after how many years , assuming no further losses , will the forest exceeds its original acreage ?
(A) 10 (B) 8 (C) 5 (D) 4 (E) 3
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by [email protected] » Mon Oct 17, 2016 10:05 am
Hi sucheta.lahiri,

This question can be solved in a couple of different ways. Here's how you can TEST VALUES to get to the correct answer.

Let's start with 100 acres.

We're told that 35% of the acres were destroyed in a fire...

100 - (.35)(100) = 65 acres left

Then the remainder grows at 10% a year. We're asked how long it takes to get above 100 acres....

Year 1 = 65 + (.1)(65) = 71.5 acres
Year 2 = 71.5 + (.1)(71.5) = 78.65 acres
Year 3 = 78.65 + (.1)(78.65) = about 86.5 acres
Year 4 = 86.5 + (.1)(86.5) = about 95 acres
Year 5 = 95 + (.1)(95) = about 104.5 acres

Thus, it takes 5 years to exceed the original 100 acres.

Final Answer: C

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