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?:

me! what did you put for this question?

step-by-step explanation:

you need to give us more information since we can't answer

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt