Question

A phone company charges for service according to the formula: C(n) = 19 + 0.08n , where n is the number of minutes talked , and C(n) is the monthly charge, in dollars .The rate of change in this equation is:The initial value in this equation is:

Answer 1

In a linear equation, the coefficient of the variable is the rate of change and the constant term is the initial value.

For example, a linear function with rate of change m and initial value b is:

`f(x)=mx+b`

In the given formula, the variable is n, its coefficient is 0.08 and the constant term is 19.

Since n is measured in minutes and C is measured in dollars (as well as the initial value), then, the coefficient 0.08 must have the units necessary for the minutes to cancel out, leaving dollars as the unit of 0.08n. Then, the units of the rate of change must be dollars per minute.

Since the constant term is 19, then the initial value is 19.

Therefore, the answers are:

The rate of change in the equation is 0.08 dollars per minute.

The initial value in the equation is 19 dollars.