Respuesta :
Using linear function concepts, it is found that the piece-wise function that can be used to calculate the monthly billing amount, B, for a monthly level of t text messages is:
- [tex]B(t) = 5, t \leq 250[/tex]
- [tex]B(t) = 5 + 0.1(t - 250), 250 \leq t \leq 2000[/tex]
- [tex]B(t) = 5 + 0.1(t - 250) + 0.4(t - 2000), t \geq 2000[/tex]
What is a linear function?
A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
In this problem, a piece-wise function is bought, that is, a function that has different definitions according on the input.
Up to 250 text messages:
- A flat rate of $5.00 each month is paid, that is, the y-intercept is [tex]b = 5[/tex], while the slope is 0, and the function is:
[tex]B(t) = 5, t \leq 250[/tex]
Between 250 and 2000 text messages:
- For each additional message over 250, the customer pays $0.1, that is, a slope of [tex]m = 0.1[/tex] multiplied by t - 250 is added to the function, hence:
[tex]B(t) = 5 + 0.1(t - 250), 250 \leq t \leq 2000[/tex]
Above 2000 text messages:
- For each additional message over 2000, the customer pays $0.4, that is, a slope of [tex]m = 0.4[/tex] multiplied by t - 2000 is added to the function, hence:
[tex]B(t) = 5 + 0.1(t - 250) + 0.4(t - 2000), t \geq 2000[/tex]
Hence, the piece-wise function is:
- [tex]B(t) = 5, t \leq 250[/tex]
- [tex]B(t) = 5 + 0.1(t - 250), 250 \leq t \leq 2000[/tex]
- [tex]B(t) = 5 + 0.1(t - 250) + 0.4(t - 2000), t \geq 2000[/tex]
You can learn more about linear function concepts at https://brainly.com/question/24808124
