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tree growth

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tree growth

by AMat700 » Wed Feb 16, 2011 3:03 pm
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height increase each year?

A) 3/10
B) 2/5
C) 1/2
D) 2/3
E) 6/5

Answer: 2/3 (I actually can't remember the correct answer, but I believe it was most likely 2/3)

How do you solve this?

Thanks.
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by aleph777 » Wed Feb 16, 2011 3:33 pm
AMat,

This is a linear growth problem, which we know because it says the tree "increased by a constant amount." So we know from the start that we should use the linear growth formula: y=mx+b where b is the original or base value, m is time, and x is the constant growth rate.

The question tells us b = 4 (that was the size of the tree when it was first planted).

And we know that after 6 years the tree would be equal to:

y=6x+4 (six year multiplied by a constant growth rate of x added to the initial height of 4 feet tall).

We also know that at the size of the tree at 6 years is 1/5 taller than the height of the tree at 4 years, and we can be sure the height at 4 years is:

y=4x+4.

So now we can set the two equal. The key is that the height at 6 years is equal to the height at 4 years PLUS 1/5 of the height at 4 years. So the final equation would look like this:

6x+4 = 4x+4+[1/5(4x+4)]
2x = (4x+4)/5
10x = 4x+4
6x = 4
x = 4/6 = 2/3

And x is the answer, because the question asks for the change each year.
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by ankur.agrawal » Thu Feb 17, 2011 5:01 am
Life saver Approach:

Put in the answer choices & check. Its faster than what we initially think.

'D'



AMat700 wrote:When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height increase each year?

A) 3/10
B) 2/5
C) 1/2
D) 2/3
E) 6/5

Answer: 2/3 (I actually can't remember the correct answer, but I believe it was most likely 2/3)

How do you solve this?

Thanks.
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