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Question 214676: media services charges $20 for a phone and $30/month for its economy plan. What is the total cost of C (t) of operating a media service phone for t months?
C(t)=
what is the total cost for 7 months of service?
C(t)=
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Any linear function can be written in the form
 where 'm' is the slope and represents the change of the function and 'b' is the initial value of the function.
In our case, the change is $30 (since the total cost goes up $30 a month) while the initial fee is $20. So this means  and  giving us the function 
If you're unsure of the answer, simply plug in values of 't'
Examples: When  , the number of months is zero. So this represents the start of the plan. Plug this into C(t) to get  . So no matter what, you're going to pay $20 up front (which is exactly what the problem states).
Now one month later, the value of 't' is now  . If you simply add $30 to the down payment of $20, you get $50. In other words, you've paid $50 for the first month. If we plug in t=1, we get  which is exactly what we just got.
So you may be asking why we're going through all the trouble of using functions when we could just add. Using functions will save us time for larger values of 't'. For instance, let's say you want to know what the total cost will be 20 months from now. Are you going to add 20 sets of $30 to 20 to find the answer? You could, but why do that when you can simply use the function. Also, you can also answer other questions that the previous technique would have a hard time doing so.
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To find the cost of 7 months of service, just plug in t=7:
Start with the given function.
 Plug in 
 Multiply
 Add
So 7 months of service will cost $230
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