Question

Taylor charges $15 for the first hour of dog walking and $10 for each additional hour or fraction of an hour. The rates that Lucy charges for x hours of dog walking are modeled with the function shown.

f(x) = LaTeX: \lbrace{LaTeX: \begin{matrix}\text{20x, 0 ≤ x ≤ 2}\\\text{10x, 2 4}\end{matrix}20x, 0 ≤ x ≤ 2 10x, 2 4


Who will charge more to walk a dog for 2.5 hours, Taylor or Lucy? How much more?


Who?:


How much more?:

Answer 1

Taylor will charge more by $15

Explanation:

Given

Taylor

First Hour = $15

Hourly Rate = $10

Lucy:

`f(x) = \left \{ {{20x,\ 0 \le \ x \ \le 2} \atop {10x, x>2}} \right.`

For a dog walk of 2.5 hours.

Taylor's charges is:

`Charges = First\ Hour + Hourly\ Rate * 2.5`

`Charges = \$15 + \$10 * 2.5`

`Charges = \$15 + \$25`

`Charges = \$40`

Lucy's charges is:

Here, we consider

`f(x) = 10x` Because
`x > 2`

i.e 2.5 > 2

So, Lucy's charges is:

`Charges = 10 * \$2.5`

`Charges = \$25`

By comparison;

Taylor will charge more by $15

The difference is calculated by:

`Difference = \$40 - \$25`

`Difference = \$15`