Question

The function LaTeX: c\left(t\right)=1.75+0.85\left(t-1\right)c ( t ) = 1.75 + 0.85 ( t − 1 ) represents the cost to call China as a function of the time, in minutes, t, on the phone. When will the cost first exceed $57?

Answer 1

Given:

The cost to call China as a function of the time, in minutes, t, on the phone is

`c(t)=1.75+0.85(t-1)`

To find:

The time when the cost first exceed $57.

Solution:

The cost first exceed $57 means cost is greater than $57.

`c(t)>57`

`1.75+0.85(t-1)>57`

`0.85(t-1)>57-1.75`

`0.85(t-1)>55.25`

Divide both sides by 0.85.

`t-1>(55.25)/(0.85)`

`t-1>65`

`t>65+1`

`t>66`

Therefore, after 66 minutes the cost to call china will exceed $57. It means first at t=67 the cost will exceed $57.