Question

Let x be the number of long distance calls (in minutes) in a month, and let C(x) be the total monthly long distance charge (in dollars). Determine the monthly long distance charge for 120 minutes.

C(x)= { 30 if 5 ≤ x ≤ 100
{ 30 + 0.10(x-100) if x >100

Answer 1

To calculate the monthly long distance charge for 120 minutes, apply the piecewise function C(x) = 30 + 0.10(x - 100) for minutes over 100, resulting in a $32 charge.

Step-by-step explanation:

To determine the monthly long distance charge for 120 minutes, we use the given function C(x). Since the number of minutes (120) is greater than 100, we apply the second part of the function: C(x) = 30 + 0.10(x - 100). Plugging in 120 minutes for x, we calculate the charge as follows:

The monthly long distance charge, C(x), is defined as follows:

C(x) = 30 if 5 ≤ x ≤ 100

C(x) = 30 + 0.10(x-100) if x > 100

To determine the monthly long distance charge for 120 minutes, we need to plug in x = 120 into the equation.

C(120) = 30 + 0.10(120 - 100) = 30 + 0.10(20) = 30 + 2 = 32

Therefore, the monthly long distance charge for 120 minutes is $32.

C(120) = 30 + 0.10(120 - 100) = 30 + 0.10(20) = 30 + 2 = $32.

Therefore, the total monthly long distance charge for 120 minutes is $32.