Question 1208727
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Part A


x = number of scooters manufactured
300x = additional cost to make those scooters on top of the $375,000


Answer: 
C(x) = 300x+375000


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Part B


The average cost is the result of dividing the previous function over x.
Let's say for example that it cost $2,000,000 to make 5000 scooters.
The average cost per scooter would be (2,000,000)/5000 = 400 dollars.


That's how we end up with this average cost function
A(x) = (300x+375000)/x
which is the answer to part B.


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Part C


As x gets bigger and bigger, A(x) will steadily approach 300 from above.
This is because we can rewrite A(x) like so,
A(x) = (300x+375000)/x
A(x) = (300x)/x+(375000/x)
A(x) = 300 + (375000/x)
The fractional portion 375000/x at the end will slowly approach zero as x gets larger and larger. So we basically have 300 + some decimal amount. 
No matter how large x is, we will never reach 300 itself. 


Let's look at a table of values.
<table border = "1" cellpadding = "5"><tr><td>x</td><td>A(x)</td></tr><tr><td>10</td><td>37800</td></tr><tr><td>20</td><td>19050</td></tr><tr><td>50</td><td>7800</td></tr><tr><td>100</td><td>4050</td></tr><tr><td>1000</td><td>675</td></tr><tr><td>10,000</td><td>337.5</td></tr><tr><td>100,000</td><td>303.75</td></tr><tr><td>1,000,000</td><td>300.375</td></tr><tr><td>10,000,000</td><td>300.0375</td></tr><tr><td>100,000,000</td><td>300.00375</td></tr><tr><td>1,000,000,000</td><td>300.000375</td></tr></table>
We see that the results for A(x) steadily approach 300. 
We never actually arrive there. 


If you were to graph A(x), then you should see the curve slowly approach the horizontal asymptote y = 300. 
<a href="https://www.geogebra.org/calculator">GeoGebra</a> and <a href="https://www.desmos.com/calculator">Desmos</a> are two graphing options among many others.



Answer: 
The horizontal asymptote is y = 300.
It represents the floor for the average cost per scooter.
The average cost slowly approaches this value from above. 
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