Question

Did you drive to work or school today? When you are driving at a constant speed, the amount of gas left in the tank can typically be modeled by a linear equation. The equation y = -2x + 15 would represent a car that has a full 15-gallon tank and burns 2 gallons of gas an hour when x is the number of hours driven and y is the amount of gas in the tank. Find a linear relationship (equation) that you would use or rely on in your field when you receive your degree, and explain what it is and how it is used. Identify the initial condition, such as the full tank of gas above, and the rate of change. For a linear equation, the rate of change (slope) needs to be constant. If you can’t find one in your field, broaden your research to include any real-world application.

Answer 1

A real World Problem: Comparing Cell Phone Plans.

A cell phone plan costs $45.00 per month with 200 calls free in a month and , each subsequent call is charged at $ 0.05 per call. Another cell phone plan costs $55.00 per month with 300 calls free in a month and each subsequent call is charged at $ 0.03 per call. Which cell phone plan should a person choose.

Suppose a person makes x number of phone calls in a month. In the first case, the monthly phone bill is $ 45+(x-200)*0.05 = $ 35+0.05x…(1). In the second case, the monthly phone bill is $ 55 +(x-300)*0.03 = $ 46+0.03x…(2). The monthly cell phone charges are equal if 35+0.05x = 46+0.03x or, 0.02x = 9 or, x = 9/0.02 = 450. Thus, if the person makes 450 phone calls per month, then the charges for both the cell phone plans are same. If he makes less than 450 phone calls per month , then the 1^st plan is cheaper and if more than 450 phone calls are made per month , then the 2^nd plan is cheaper.