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July 20th, 2015, 09:42 AM   #1
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Exponent Word Problem

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I am trying to figure this out

Heavier aircraft require runways with thicker pavement for landing and takeoff. A pavement 6 inches thick can accommodate an aircraft weighing 80,000 lbs., whereas a 12-inch-thick pavement is necessary for a craft weighing 350,000 lbs. The relation between pavement thickness t in inches and gross weight W in thousands of lbs. is modeled by W=Ca^t

$\displaystyle W=Ca^t$

So..
(6, 80),(12,350)

a. Find values for C and a.

On my notes I have $\displaystyle 80=Ca^6 $ => $\displaystyle C=8/a^6 $

But I do not know where the 8 came from. Could anyone explain?
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July 20th, 2015, 10:04 AM   #2
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Quote:
Originally Posted by TravisR View Post
Forum:

I am trying to figure this out

Heavier aircraft require runways with thicker pavement for landing and takeoff. A pavement 6 inches thick can accommodate an aircraft weighing 80,000 lbs., whereas a 12-inch-thick pavement is necessary for a craft weighing 350,000 lbs. The relation between pavement thickness t in inches and gross weight W in thousands of lbs. is modeled by W=Ca^t

$\displaystyle W=Ca^t$

So..
(6, 80),(12,350)

a. Find values for C and a.

On my notes I have $\displaystyle 80=Ca^6 $ => $\displaystyle C=8/a^6 $

But I do not know where the 8 came from. Could anyone explain?
Your notes are wrong. If $\displaystyle 80= Ca^6$, then $\displaystyle C= 80/a^6$. "80" not "8". You are just dividing both sides by $\displaystyle a^6$.
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July 20th, 2015, 11:00 AM   #3
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Well that makes sense then.

So to begin solving this problem would I go like this:

$\displaystyle f(350)/f(80) = a^6 ; f(350)/f(80) = 350/80 = 35/8 $

Then

$\displaystyle W = C(35/^x $

Last edited by TravisR; July 20th, 2015 at 11:03 AM.
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