Using Function Notation to Describe Rules

Question

The college student who is looking for a data plan for her cell phone found a third option, which also offers a 2 gigabyte monthly allowance for data.

The monthly cost of this option can be represented by function , defined by: , where  is the gigabytes of data used over the monthly allowance.

1. Find  and explain what it means in this situation.
2. Her budget is still $50 a month. To find out how many gigabytes of data she could use if she chose this plan, she writes  and solves for  What value of  makes this equation true? Show your reasoning.

Answer 1

1) To find C(0.7), we plug in 0.7 for x in the equation.

C(0.7) = 30(0.7) + 5

We then solve this equation and find that C(0.7) = 26

2) To find x, we have to plug C(x) = 50 into our initial equation

50 = 30x + 5

Our first step is to subtract 5 from both sides, which gives us

45 = 30x

Dividing both sides by 30 gives us our answer

3/2 = x = 1.5

As x is the number of gigabytes OVER the 2 gigabyte monthly allowance, to find the total number of gigabytes we have to add 2 and 1.5, and we find that she could use 3.5 gigabytes of data.

Answer 2

Consider all the info you are given:

The monthly allowance is 2 GB...this is basically how much data is included in the the plan so that the monthly pymt is the same every month. When the GBs used goes pass 2GB...there is a cost to that.

1. You're given C(x) = 30x + 50, the monthly cost of the plan
2. 'x' is the GB of data used OVER the allowance (2GB.)

They put over in italics to give you a hint to the solution.

(a) C(0.7) is the cost when the data used goes over 2GB by 0.7 GB. C(0.7) = 30(0.7) + 5 = 26

The college student would pay $26 when they use an extra 0.7GBs (pass the allowance.)

(b) This part to the problem wants you to figure out how much the overage, pass the 2GBs, the college student can go and only end up paying $50 (the set budget)

So you the solve for x by setting C(x) = 50

30x + 5 = 50

30x = 50 - 5 = 45

x = 45/30

x = 1.5

Remember x is the overage (the GBs over the allowances), so to stay at budget, the college student can use 3.5 GBs of data (2GBs + 1.5 GBs) only pay $50 that month.

Hope this helps...