Question

Amy owns Amy's donuts. She needs a baker and decides to place a classified ad in the paper. The cost of an ad is x lines long is given by the following piecewise function. Find the cost of 5 lines.c(x)=20 when x <\ (less than or equal to) 420+6(x-4) when x>4

Answer 1

The piecewise function for the cost of the ad "c" that depends on the number of lines "x" is:

`\begin{gathered} c(x)=20,\text{ when x}\leq4 \\ c(x)=20+6(x-4),\text{ when x>4} \end{gathered}`

The first piece of the function is useful to calculate the cost of 1, 2, 3, or 4 lines. Remember that "x" is the number of lines.

But since we need to calculate the cost of 5 lines, we are going to need the second piece of the function:

`c(x)=20+6(x-4)`

Because the condition to use it is that x is greater than 4, and since 5 is greater than 4, we can use it.

Thus, substitute x=5 into the function:

`\begin{gathered} c(x)=20+6(x-4) \\ \text{Substituting x=5} \\ c(5)=20+6(5-4) \end{gathered}`

And solve the operations. First, solve the subtraction inside the parenthesis:

`c(5)=20+6(1)`

Now, solve the multiplication 6(1) which is equal to 6:

`c(5)=20+6`

And finally, add 20 and 6:

`c(5)=26`

The cost of an ad with 5 lines is $26

Answer: $26