High School

Emma hired a contractor to install a new brick patio in her backyard. The original quote was $832. However, Emma decided to make the patio wider. The cost of expanding the patio is $13 per square foot.

Write an equation for the function that describes the total cost of the patio if she decides to expand it by \(x\) square feet. If the function is linear, write it in the form [tex]f(x) = mx + b[/tex]. If it is exponential, write it in the form [tex]f(x) = a(b)^x[/tex].

Answer :

Answer: The linear function representing the total cost of the patio is:

f(x) = 13x + 832

Step-by-step explanation:

The total cost of the patio consists of the original quote and the additional cost for expanding it by x square feet. Since the cost of expanding the patio is given in dollars per square foot, this relationship is linear. We can write a linear function in the form f(x) = mx + b, where:

  • f(x) represents the total cost of the patio.
  • m is the slope (rate of change) of the function, which corresponds to the cost per square foot of expanding the patio.
  • x is the number of additional square feet Emma decides to expand the patio.
  • b is the y-intercept, representing the original quote.

In this case, the slope m is $13 per square foot, and the y-intercept b is the original quote of $832. So the linear function representing the total cost of the patio is:

f(x) = 13x + 832