SOLUTION: A company manufactures an alarm clock. Three weeks ago the had 250 on hand. Two weeks from now it will have 500. Assume the company will continue to make the clocks at this same ra

Algebra ->  Expressions-with-variables -> SOLUTION: A company manufactures an alarm clock. Three weeks ago the had 250 on hand. Two weeks from now it will have 500. Assume the company will continue to make the clocks at this same ra      Log On


   

Question 318683: A company manufactures an alarm clock. Three weeks ago the had 250 on hand. Two weeks from now it will have 500. Assume the company will continue to make the clocks at this same rate.
I have tried many different ways to write the expression and none of them work. Please anyone help. Thank You
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let t=0 be three weeks ago, N=250.
Let t=5 be 2 weeks from now, N=500.
t is measured in weeks, N is the number of alarm clocks.
Find the slope.
m=%28N2-N1%29%2F%28t2-t1%29=%28500-250%29%2F%285-0%29=250%2F5=50
Use the point-intercept form of a line, y=mx%2Bb
N=50t%2Bb
Use either point to solve for b.
250=50%280%29%2Bb
b=250
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highlight%28N%28t%29=50t%2B250%29
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You could also have said t=0 is now.
2 weeks ago would have been t=-2.
3 weeks from now would be t=3.
The slope is the same.
The equation changes slightly to,
N=50t%2Bb
250=50%28-2%29%2Bb
b=350
N%28t%29=50t%2B150
So 2 weeks ago, t=-2
N%28-2%29=-100%2B350=250
and 3 weeks from now, t=3
N%283%29=50%283%29%2B350=500
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It all depends on how you define your variable t.