Respuesta :
Answer:
The remaining credit after 61 minutes of calls is $20.85.
Step-by-step explanation:
The credit remaining after t minutes can be modeled by a linear function is the following format:
[tex]C(t) = C(0) - at[/tex]
In which C(0) is the initial amount of credit and a is the cost of a minute.
The remaining credit after 42 minutes of calls is $23.70
This means that [tex]C(42) = 23.70[/tex]
So
[tex]C(t) = C(0) - at[/tex]
[tex]23.70 = C(0) - 42a[/tex]
[tex]C(0) = 42a + 23.70[/tex]
The remaining credit after 53 minutes of calls is $22.05.
This means that [tex]C(53) = 22.05[/tex]
So
[tex]C(t) = C(0) - at[/tex]
[tex]22.05 = C(0) - 53a[/tex]
[tex]C(0) = 22.05 + 53a[/tex]
From above:
[tex]C(0) = 42a + 23.70[/tex]
So
[tex]42a + 23.70 = 22.05 + 53a[/tex]
[tex]11a = 1.65[/tex]
[tex]a = \frac{1.65}{11}[/tex]
[tex]a = 0.15[/tex]
[tex]C(0) = 42*0.15 + 23.70 = 30[/tex]
So
[tex]C(t) = C(0) - at[/tex]
[tex]C(t) = 30 - 0.15t[/tex]
What is the remaining credit after 61 minutes of calls?
This is C(61).
[tex]C(t) = 30 - 0.15*61 = 20.85[/tex]
The remaining credit after 61 minutes of calls is $20.85.
