document.write( "Question 1208727: A scooter manufacturing company has a monthly fixed cost of $375,000 along with an additional $300 for each scooter made.
\n" ); document.write( "A) Write the monthly cost function C for producing scooters
\n" ); document.write( "B) Write the Average Cost equation using the Cost function C in part A) for the number of scooters X
\n" ); document.write( "C) What is the Horizontal Asymptote for the Average Cost function? What does it represent?
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Algebra.Com's Answer #847145 by math_tutor2020(3817) $\"\"$ $\"About$

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\n" ); document.write( "Part A\r
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\n" ); document.write( "\n" ); document.write( "x = number of scooters manufactured
\n" ); document.write( "300x = additional cost to make those scooters on top of the $375,000\r
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\n" ); document.write( "\n" ); document.write( "Answer:
\n" ); document.write( "C(x) = 300x+375000\r
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\n" ); document.write( "Part B\r
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\n" ); document.write( "\n" ); document.write( "The average cost is the result of dividing the previous function over x.
\n" ); document.write( "Let's say for example that it cost $2,000,000 to make 5000 scooters.
\n" ); document.write( "The average cost per scooter would be (2,000,000)/5000 = 400 dollars.\r
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\n" ); document.write( "\n" ); document.write( "That's how we end up with this average cost function
\n" ); document.write( "A(x) = (300x+375000)/x
\n" ); document.write( "which is the answer to part B.\r
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\n" ); document.write( "Part C\r
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\n" ); document.write( "\n" ); document.write( "As x gets bigger and bigger, A(x) will steadily approach 300 from above.
\n" ); document.write( "This is because we can rewrite A(x) like so,
\n" ); document.write( "A(x) = (300x+375000)/x
\n" ); document.write( "A(x) = (300x)/x+(375000/x)
\n" ); document.write( "A(x) = 300 + (375000/x)
\n" ); document.write( "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.
\n" ); document.write( "No matter how large x is, we will never reach 300 itself. \r
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\n" ); document.write( "\n" ); document.write( "Let's look at a table of values.
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x	A(x)
10	37800
20	19050
50	7800
100	4050
1000	675
10,000	337.5
100,000	303.75
1,000,000	300.375
10,000,000	300.0375
100,000,000	300.00375
1,000,000,000	300.000375

\n" ); document.write( "We see that the results for A(x) steadily approach 300.
\n" ); document.write( "We never actually arrive there. \r
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\n" ); document.write( "\n" ); document.write( "If you were to graph A(x), then you should see the curve slowly approach the horizontal asymptote y = 300.
\n" ); document.write( "GeoGebra and Desmos are two graphing options among many others.\r
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\n" ); document.write( "\n" ); document.write( "Answer:
\n" ); document.write( "The horizontal asymptote is y = 300.
\n" ); document.write( "It represents the floor for the average cost per scooter.
\n" ); document.write( "The average cost slowly approaches this value from above.
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