Question

A telephone company charges $30 a month and gives the customer 200 free minutes. After the 200 min, the company charges $0.03 a minute.

(a) Write the function using function notation.
(b) Find the cost for talking 350 min in a month
(c) Find the number of minutes used if the monthly charge is $34.68

Answer 1

(a)

f(x) = 30, for x ≤ 200

f(x) = 0.03(x - 200) + 30, for x > 200

(b) $34.50

(c) 356

Explanation:

Let x = number of minutes.

(a)

f(x) = 30, for x ≤ 200

f(x) = 0.03(x - 200) + 30, for x > 200

(b)

Here, x = 350, so x > 200.

f(x) = 0.03(x - 200) + 30

f(350) = 0.03(350 - 200) + 30

f(350) = 0.03(150) + 30

f(350) = 4.5 + 30

f(350) = 34.5

$34.50

(c)

f(x) = 0.03(x - 200) + 30

0.03(x - 200) + 30 = 34.68

0.03(x - 200) = 4.68

x - 200 = 156

x = 356