Question

A health club charges a one time initiation fee of $120.00 plus a membership fee of $30.00 per month. a. Write an expression for the cost function C(x) that gives the total for membership at the health club for x months. b. Draw a graph of the function in (a).c. The health club decided to give it's member an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, use a different color and draw on the same set of axes the cost graph under the plan. d. Determine after how many months the second plan is less expensive for the member. a. C(x) = _______ (Do not factor)

Answer 1

a.

Given that a health club charges a one-time initiation fee of $120.00 plus a membership fee of $30.00 per month.

The total cost will be equal to the fixed one-time charge plus the charge per month times the number of months.

It can be represented by the expression C(x);

`C(x)=120+30x`

b.

Graphing of the function, we would have;

c.

If the health club decided to give its members an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, we will have the function as;

`F(x)=420+10x`

graphing the above function, we have;

the first plan is represented by the blue line while the second plan is represented by the red line.

d.

The number of months after which the second plan is less expensive is the value of x when the two lines meet.

the two lines meet at point;

`(15,570)`

The value of the x coordinate is 15.

So, The number of months after which the second plan is less expensive is

`15\text{ months}`