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