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) =

{

20x, 0
10x. 2
5x, x >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

The answer is below

Explanation:

Let x represent the number of hours of dog walking. Taylor charges $15 for the first hour and $10 for each additional hour. Therefore:

Let g(x) represent how much Taylor charges. Hence:

g(x) = 15 for 0 ≤ x ≤ 1

g(x) = 15 + 10(x - 1) = 15 + 10x - 10 = 10x + 5 for x > 1

g(x) can be represented by the piecewise function:

`g(x)=\left \{ {{15\ \ \ \ \ \ for\ 0\leq x\leq 1} \atop {10x+5\ \ for\ x>1}} \right.`

Lucy charges f(x) is modeled by the piecewise function:

`f(x)=\left \{ {{20x\ \ \ \ \ \ for\ 0\leq x\leq 2} \atop {10x\ \ \ for\ 0< x< 4}} \right.`

Therefore the charge for walking a dog for 2.5 hours by either Taylor or Lucy is:

For Taylor; f(2.5) = 10(2.5) + 5 = $30

For Lucy; g(2.5) = 10(2.5) = $25

Therefore Taylor charges more by walking a dog for 2.5 hours. Taylors charge is $5 more than Lucy charge ($30 - $25).