Question 208178: 1. A company finds that it can produce 10 solar heaters for $7500 while the production of 20 heaters costs $13,900. If cost is a linear function of the number of heaters produced, express the cost function C(x) where x is the number of heaters produced.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 1. A company finds that it can produce 10 solar heaters for $7500 while the production of 20 heaters costs $13,900. If cost is a linear function of the number of heaters produced, express the cost function C(x) where x is the number of heaters produced.
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The problem gives you two points in the equation:
(10,7500)
(20,13900)
.
And, since they said it was "linear" it fits the "slope-intercept" form
y = mx + b
.
7500 = m(10) + b
13900 = m(20) + b
.
Rewriting the two equations:
7500 = 10m + b
13900 = 20m + b
.
Applying the "addition method" we multiply the top equation by -1 and add:
-7500 = -10m - b
13900 = 20m + b
-------------------
6400 = 10m
640 = m
.
Using the top equation and the definition of m above:
7500 = 10(640) + b
7500 = 6400 + b
1100 = b
.
Pulling it back together we have:
y = 640x + 1100
or
C(x) = 640x + 1100 (this is what they're looking for)
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