Question

fees are listed in the table.23.Cathy's Pet Sitting Service# of DaysPet-SittingFee1$7.502$15.003$22.504$30.005$37.50What will Cathy charge to pet sit for 8 days?A $67.50B $60.00C $52.50D $45.00

Answer 1

B $60.00

Explanation:

The cost per day is a linear function in the following format:

y = ax + b

In which y is the cost of x days of pet-sitting, a is the daily cost and b is the fixed cost.

We select two days two build the function.

1 day costs $7.50. So we have the point (1,7.5)

2 days cost $15. So we have the point (2,15).

(1,7.5)

This means that when x = 1, y = 7.5. So

y = ax + b

7.5 = a*1 + b

a + b = 7.5

b = 7.5 - a

(2,15)

This means that when x = 2, y = 15. So

y = ax + b

15 = a*2 + b

2a + b = 15.

Since b = 7.5 - a

2a + b = 15.

2a + 7.5 - a = 15

2a - a = 15 - 7.5

a = 7.5

And

b = 7.5 - a = 7.5 - 7.5 = 0

So the cost of x days of pet-sitting is:

y(x) = 7.5x

8 days:

This is y when x = 8. So

y(x) = 7.5x

y(8) = 7.5*8 = 60

The answer is B.