High School

Bill wants to replace the shingles on his roof. He goes to his local home-improvement store and finds that it costs $125 for 100 square feet of asphalt shingles.

Write an equation for the function that describes the cost of \(x\) square feet of shingles. If it is linear, write it in the form \(h(x) = mx + b\). If it is exponential, write it in the form \(h(x) = a(b)^x\).

Answer :

The cost function for replacing shingles is linear and given by h(x) = 1.25x, where 1.25 is the cost per square foot and x represents the number of square feet.

The cost function is linear since the price per square foot is constant. Therefore, we can write it in the form h(x) = mx + b, where m represents the cost per square foot and b is the initial cost or fixed expenses. Here, there are no initial costs, so b = 0.

First, we determine the cost per square foot:

  • Cost per 100 square feet = $125
  • Cost per 1 square foot = $125 / 100 = $1.25

Thus, the equation describing the cost of x square feet of shingles is:

h(x) = 1.25x

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