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?:

Question

contestada

Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-02-04T02:17:13+01:00

Answer:

Taylor will charge more by $15

Step-by-step explanation:

Given

Taylor

First Hour = $15

Hourly Rate = $10

Lucy:

[tex]f(x) = \left \{ {{20x,\ 0 \le \ x \ \le 2} \atop {10x, x>2}} \right.[/tex]

For a dog walk of 2.5 hours.

Taylor's charges is:

[tex]Charges = First\ Hour + Hourly\ Rate * 2.5[/tex]

[tex]Charges = \$15 + \$10 * 2.5[/tex]

[tex]Charges = \$15 + \$25[/tex]

[tex]Charges = \$40[/tex]

Lucy's charges is:

Here, we consider

[tex]f(x) = 10x[/tex] Because [tex]x > 2[/tex]

i.e 2.5 > 2

So, Lucy's charges is:

[tex]Charges = 10 * \$2.5[/tex]

[tex]Charges = \$25[/tex]

By comparison;

Taylor will charge more by $15

The difference is calculated by:

[tex]Difference = \$40 - \$25[/tex]

[tex]Difference = \$15[/tex]