Writing a rational function representing Average cost over time. (Pre-Calc)

Question

I have a linear function that is C(t) = 4999.99 + 36(t)

where C(t) = Cost @ year after purchase

And t = years since purchase

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AC(t) = (4,999.99 +36(t)) / (t)

(This is my funciton)

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But, acording to my projects description. AC(t) (average cost over time is AC(t) = C(t) / t

but every time i graph it i get something that looks like this

But i know it needs to look something like a curve.

Im confused since the projects description says to do this:

⦁   The average cost, in dollars per year, AC(t)  , will turn out to be the total cost divided by  . AC(t)   is a rational function.  Write the rational function representing the average cost function per year for your device.

Answer 1

You are doing fine. The total cost is $5000$ at the start and $36$ per year thereafter. The average cost starts very high and decreases as the $5000$ gets averaged over more years. It would be better to plot your curve over a range like $0-10$ or $0-30$, not up into the hundreds. You can write the average cost as $\frac {5000}t+36$ and you can see that at $t=1$ it will be $5036$, at $t=2$ it will be $2518$ and so on.