A cellphone company offers two plans. Plan A costs $40 a month for the first 60 minutes, and $0.3 for each additional minute. Plan B costs $70 a month for the first 175 minutes and $0.28 for each additional minute.
(a) Find a piecewise function CA(t) that determines the total cost CA per month in dollars using t minutes.
To find the piecewise function CA(t) that determines the total cost per month using t minutes, we need to consider the cost for both the plans A and B.
For Plan A:
The cost for the first 60 minutes is $40.
For each additional minute beyond 60 minutes, the cost is $0.3.
For Plan B:
The cost for the first 175 minutes is $70.
For each additional minute beyond 175 minutes, the cost is $0.28.
Now, let's write the piecewise function:
For Plan A, if t is less than or equal to 60 minutes:
CA(t) = $40
For Plan A, if t is greater than 60 minutes:
CA(t) = $40 + ($0.3 * (t - 60))
For Plan B, if t is less than or equal to 175 minutes:
CA(t) = $70
For Plan B, if t is greater than 175 minutes:
CA(t) = $70 + ($0.28 * (t - 175))
So, the piecewise function CA(t) can be written as:
CA(t) = $40, if t ≤ 60
$40 + ($0.3 * (t - 60)), if t > 60
$70, if t ≤ 175
$70 + ($0.28 * (t - 175)), if t > 175