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August 19th, 2011, 08:05 AM   #1
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Relation?

What is the relation of these values? I can't figure it out.

For a child between the ages of 6 and 16, its
height y (in inches) is approximately a linear
function of age t (in years). Joe Smithís son
John was 40 inches tall at age 6 and 58 inches
tall at age 10.
Estimate Johnís height at age 15.
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August 19th, 2011, 08:43 AM   #2
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Re: Relation?

You are told essentially that:

y(t) = mt + b

For John, you are given:

y(6) = 40

y(10) = 58

This results in the linear system:

(1) 6m + b = 40

(2) 10m + b = 58

Subtracting (1) from (2) we find:

4m = 18

m = 18/4 = 9/2

6(9/2) + b = 40

b = 13

Thus, for John, we have:

y(t) = (9/2)t + 13

To estimate John's height at age 15, we use:

y(15) = (9/2)15 + 13 = 80.5
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August 19th, 2011, 09:06 AM   #3
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Re: Relation?

You're seriously a big help. Thanks!
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August 21st, 2011, 12:18 PM   #4
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Re: Relation?

As m = 9/2 is determined, like [color=#00FF00]MarkFL[/color] / you did, John grows for 5 more years after his tenth. So his length is estimated at (58 + 5 * 9/2) inches = 80.5 inches.
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