Question

a cell phone plan costs $200 to start. Then there is a $50 charge each month. what is the total cost (start up fee and monthly charge) to use the cell phone plan for one month?I got $250Part Bwhat is the total cost for x months?Part DIs there a proportional relationship between time and cost of the cell phone plan? Explain how you know.Part E what is the start-up fee and monthly cost for this plan?

Answer 1

Let x be the number of months we have the cell phone plan.

We have a fixed cost, that is $200 and does not depend on the number of months.

Then, we have an additional cost of $50 per month. Then, for x months we have to add 50x of cost to the fixed $200.

We can express the cost C(x) as:

`C(x)=200+50x`

For one month (x=1), the cost is:

`C(1)=200+50\cdot1=200+50=250`

For a proportional relationship, the ratio f(x)/x has to be constant for all points of the relationship.

In this case, if C(x)/x is constant, then we have a proportional relationship.

We will calculate this as:

`(C(x))/(x)=(200+50x)/(x)=(200)/(x)+50`

As the quotient C(x)/x is not constant (it depends on the value of x), the relationship is not proportional.

We can also spot that is not a proportional relationship beacuse the point (x,y)=(0,0) does not belong to the relation.

Answer:

A) The cost for one month is $250.

B) The total cost for x months can be expressed as 200+50x.

D) No, the relation is not proportional, as the ratio between the cost and months is not constant.

E) The start-up fee is $200 and the monthly cost is $50.