Question

An additional association wants to rent a cotton candy machine for a carnaval. There is a deposit to rent it plus an additional $8 per hour. The total cost to rent the machine for 5 hours is $115. Assume the relationship is linear. Find and interpret the rate of change and initial value"

Answer 1

The rate of change is $8. Since it is positive, the more the hours the higher the total cost.

The initial value is $75 which is the fixed cost.

Explanation:

Let
`c` be the initial amount to be deposited to rent the cotton candy machine.

There is an additional cost of $8 per hour.

So for
`x` hours the total cost will be given by the linear function;

`y=8x+c`, where y is the total cost after x hours.

The total cost to rent the machine for 5 hours is $115.

This implies that;

`x=5,y=115`

We substitute these values into the equation to obtain;

`8(5)+c=115`

`\Rightarrow 40+c=115`

`\Rightarrow c=115-40`

`\Rightarrow c=75`

Therefore the rate of change is $8.

Since the rate of change is positive, the more the hours the higher the total cost.

The initial value is $75.

This is the fixed amount to deposit even though you have not started using the machine