An internet company charges 500 pesos sor first 30gb used in a month. Everybexceeding GB then cost 30 pesos.but if the customer reach a total og 50 gb and above a flat rate of 1000 pesos will be charge instead.write piecewise function
Sure, here's the piecewise function to represent the charges based on the amount of data used in a month:
Let x represent the number of gigabytes used in a month.
For 0 <= x <= 30:
f(x) = 500x
For 30 < x < 50:
f(x) = 500(30) + 30(x - 30) = 15000 + 30x - 900 = 14100 + 30x
For x >= 50:
f(x) = 1000
So the piecewise function is:
f(x) =
500x for 0 <= x <= 30
14100 + 30x for 30 < x < 50
1000 for x >= 50
Hope that helps! Let me know if you need anything else, and I'll be happy to assist you.
To write a piecewise function for the given scenario, we need to define separate cases based on the amount of data used.
Let's denote the amount of data used as "x" in GB.
Case 1: If x is less than or equal to 30GB, the cost is a flat rate of 500 pesos. This is the initial 30GB.
Function for case 1:
f(x) = 500
Case 2: If x is greater than 30GB but less than or equal to 50GB, there is an additional cost of 30 pesos per exceeding GB.
Function for case 2:
f(x) = (x - 30) * 30 + 500
Case 3: If x is greater than 50GB, a flat rate of 1000 pesos is charged.
Function for case 3:
f(x) = 1000
Now, we can combine all the cases using the piecewise function notation:
f(x) = {500 if x ≤ 30
(x - 30) * 30 + 500 if 30 < x ≤ 50
1000 if x > 50