Question

For all three water parks the cost of a function of numbers of right compare the functions for all three water parks in terms of the rate and change describe the impact it has on the total cost of the attending of each park

Answer 1

See Explanation

Explanation:

Given

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First, we determine the cost function for all the three rides.

Ride A

From the graph, we have the following points

`(x_1,y_1) = (0,8)`

`(x_2,y_2) = (2,12)`

Calculate slope

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (12-8)/(2-0)`

`m = (4)/(2)`

`m =2` --- This represents the rate per ride

The equation is the calculated as:

`y = m(x - x_1) + y_1`

So, we have:

`y = 2(x - 0) + 8`

`y = 2(x) + 8`

`y = 2x + 8`

So, the cost function is:

`C(x) =2x + 8`

Calculate the cost of admission i.e. x=0

`C(0) = 2*0+8 = 8`

So, we have:

`C(0) = 8` --- Admission Charge

`C(x) =2x + 8` --- Cost function

`m =2` --- Rate per ride

Ride B

From the table, we have the following points

`(x_1,y_1) = (0,12)`

`(x_2,y_2) = (4,15)`

Calculate slope

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (15-12)/(4-0)`

`m = (3)/(4)`

`m = 0.75` --- This represents the rate per ride

The equation is the calculated as:

`y = m(x - x_1) + y_1`

So, we have:

`y = 0.75(x - 0) + 12`

`y = 0.75(x) + 12`

`y = 0.75x + 12`

So, the cost function is:

`C(x) = 0.75x + 12`

Calculate the cost of admission i.e. x=0

`C(0) = 0.75*0 + 12=12`

So, we have:

`C(0) =12` --- Admission Charge

`C(x) = 0.75x + 12` --- Cost function

`m = 0.75` --- Rate per ride

Ride C

No additional fee;

So, the cost function is;

`C(x) = 30`

In summary, we have:

Ride A

`C(x) =2x + 8` --- Cost function

`m =2` --- Rate per ride

Ride B

`C(x) = 0.75x + 12` --- Cost function

`m = 0.75` --- Rate per ride

Ride C

`C(x) = 30` --- Cost function

By comparison

Ride A has the highest rate per ride of (#2), followed by ride B with a rate of #0.75 per ride.

Ride C has no charges per ride

The impact on the total cost is that:

Ride A: People that opt for ride A will pay the least to get admitted (i.e #8) but they pay the most (i.e. #2) per each ride they take

Ride B: People that opt for ride B will pay #12 to get admitted, but they pay 0.75 per each ride they take

For A and B, the overall cost depends on the number of rides taken.

Ride C: Irrespective of the number of rides taken, people that opt for ride C will pay the same flat fee of #30