Question

A 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 C, defined by: C(x) = 25x + 8, where x is the gigabytes of data used over the monthly allowance.

Find the value of C(1.5) and EXPLAIN what it means in this situation. Show All of your work.
A. C(1.5) = -18.5; It represents the cost for using 1.5 gigabytes over the monthly allowance.
B. C(1.5) = 30; It represents the total monthly cost for 1.5 gigabytes of data.
C. C(1.5) = 0; It signifies that the first 1.5 gigabytes are free.
D. C(1.5) = -17; It denotes a discount for using 1.5 gigabytes.

Answer 1

The calculated value of C(1.5) is 45.5, which represents the additional cost of using 1.5 gigabytes of data over the monthly allowance. The provided options do not accurately reflect this calculated value.

Step-by-step explanation:

The cost function for a cell phone data plan is represented by C(x) = 25x + 8, where x is the number of gigabytes used over the monthly allowance and C(x) represents the monthly cost for that extra data usage. To calculate C(1.5), we substitute 1.5 for x in the equation:

C(1.5) = 25(1.5) + 8

C(1.5) = 37.5 + 8

C(1.5) = 45.5

This value represents the additional cost for using 1.5 gigabytes over the monthly allowance. Since the monthly allowance is 2 gigabytes, the total usage in this scenario would be 3.5 gigabytes. It is important to note that none of the options provided (A, B, C, D) correctly states the calculated cost for C(1.5); thus, the correct answer is not listed among the options.