Answer:
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.
Step-by-step explanation:
Let [tex]c[/tex] be the initial amount to be deposited to rent the cotton candy machine.
There is an additional cost of $8 per hour.
So for [tex]x[/tex] hours the total cost will be given by the linear function;
[tex]y=8x+c[/tex], where y is the total cost after x hours.
The total cost to rent the machine for 5 hours is $115.
This implies that;
[tex]x=5,y=115[/tex]
We substitute these values into the equation to obtain;
[tex]8(5)+c=115[/tex]
[tex]\Rightarrow 40+c=115[/tex]
[tex]\Rightarrow c=115-40[/tex]
[tex]\Rightarrow c=75[/tex]
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
