Question

A phone company has a monthly cellular data plan where a customer pays a flat monthly fee of $10 and then a certain amount of money per megabyte (MB) of data used on the phone. If a customer uses 20 MB, the monthly cost will be $11.20. If the customer uses 130 MB, the monthly cost will be $17.80. a. Find a linear equation for the monthly cost of the data plan C as a function of x, the number of MB used. Enter equation without any spaces between alphanumeric characters and signs. Enter any decimal values less than 1 with a "0" before the decimal point. Examples of correctly-entered response are C=2x+5 C=0.03x–22 C=–4x+0.35 b. Use your equation to find the total monthly cost (in $) if 250MB are used. Enter number value only (no "$" sign) with answer rounded to nearest cent (2 places after decimal)

Answer 1

As per the phone company’s monthly cellular data plan, a customer pays a flat monthly fee of $10 and then a certain amount of money per megabyte (MB) of data used. If a customer uses 20 MB, the monthly cost will be $11.20 and if the customer uses 130 MB, the monthly cost will be $17.80.

a. Let the required linear equation for the monthly cost of the data plan C(x) be C(x) = mx +b, where x is the number of MB used , m is the slope and b is an arbitrary real number. Now, when x = 0, C(x) = $ 10 so that b = 10. Then C(x) = mx+10. Further, m = ( 17.80-11.20)/ ( 130-20) = 6.60/110 = 0.06. Hence the required linear equation is 0.06x+10.

b. Further, if x = 250MB, then C(x) = 0.06*250+10 = $ 25.