Question

Paul is comparing two high-speed Internet service providers (ISPs) for his business. The graph represents the cost of each ISP as a function of t, the duration in months of a service contract.

If C(t) = 180 + 10t represents ISP A and C(t) = 25t represents ISP B, how long would the service contracts need to be for the total costs to be the same?


6 months

8 months

10 months

12 months

Answer 1

12 months, plug it in to find both equal to 300

Answer 2

The correct option is 4. The total costs will be the same at 12 months.

Explanation:

The given equations represents the cost of each ISP as a function of t, the duration in months of a service contract.

ISP A:

`C(t)=180+10t`

ISP B:

`C(t)=25t`

Equate both the functions to find the time at which the total costs to be the same.

`180+10t=25t`

Subtract 10t from both the sides.

`180+10t-10t=25t-10t`

`180=15t`

Divide both sides by 15.

`(180)/(15)=t`

`12=t`

The total costs will be the same at 12 months. Therefore the correct option is 4.