Respuesta :
Answer:
[tex]C_{1}(t) = 0.24*t[/tex]
[tex]C_{2}(t) = 34.95 + 0.12*t[/tex]
291.25 talk minutes would produce the same cost for both plans.
Step-by-step explanation:
Both plans can be modeled by a first order equation in the following format:
[tex]C(t) = C_{0} + f*t[/tex]
In which [tex]C_{0}[/tex] is the initial cost, f is the fee that is paid for each minute, and t is the number of minutes.
Cost of the first plan:
The problem states that the first plan charges a rate of 24 cents per minute, which means that [tex]f = 0.24[/tex].There is no initial cost, so [tex]C_{0} = 0[/tex].
The equation for this plan is:
[tex]C_{1}(t) = 0.24*t[/tex]
Cost of the second plan:
The problem states that the second plan charges a monthly fee of $34.95 plus 12 cents per minute. So [tex]C_{0} = 34.95[/tex] and [tex]f = 0.12[/tex]
The equation for this plan is:
[tex]C_{2}(t) = 34.95 + 0.12*t[/tex]
Find the number of talk minutes that would produce the same cost for both plan:
This is the instant t in which:
[tex]C_{1}(t) = C_{2}(t)[/tex]
[tex]0.24t = 34.95 + 0.12t[/tex]
[tex]0.12t = 34.95[/tex]
[tex]t = \frac{34.95}{0.12}[/tex]
[tex]t = 291.25[/tex]
291.25 talk minutes would produce the same cost for both plans.
