a cell phone company offers the following plan: monthly charge (which includes 500 minutes) for $40 and a charge for additional minutes will be 5 cents a minute. write a piecewise function function putting x&y terms that can be used in any # or minutes.
I am coming up with y=.05x+40 when x>500. Although I'm not sure.
close. You forgot the first piece
y = 40 when 0 <= x <= 500
y = 40+.05x when x > 500
I guess we can assume that negative minutes are to be disregarded as a possibility.
If you talk for 375 minutes in a month how much is your monthly bill
You are correct! The piecewise function for the given cell phone plan can be written as follows:
For x ≤ 500 (monthly charge of $40 includes 500 minutes):
y = $40
For x > 500 (additional minutes charged at 5 cents per minute):
y = $0.05x + $40
So, your equation y = 0.05x + 40 is correct for x greater than 500.
You are on the right track. To write a piecewise function, we need to define the function for different ranges of minutes.
For this phone plan, we have two ranges:
1. For the first 500 minutes: there is a monthly charge of $40 that includes these 500 minutes, so the cost for any usage within this range is $0.
2. For any additional minutes beyond the initial 500: there is a charge of $0.05 per minute.
So, let's define the function based on these ranges:
For x ≤ 500 (where x is the number of minutes):
In this range, the monthly charge of $40 covers the first 500 minutes, so the cost for any number of minutes within this range is $40. Therefore, the function can be written as:
y = 40
For x > 500:
In this range, there is a charge of $0.05 per minute for any additional minutes beyond the initial 500. Therefore, the function can be written as:
y = 0.05x + 40
Overall, the piecewise function can be written as:
y =
40, if x ≤ 500
0.05x + 40, if x > 500