Question 1208727: A scooter manufacturing company has a monthly fixed cost of $375,000 along with an additional $300 for each scooter made.
A) Write the monthly cost function C for producing scooters
B) Write the Average Cost equation using the Cost function C in part A) for the number of scooters X
C) What is the Horizontal Asymptote for the Average Cost function? What does it represent?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
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.
| 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 |
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.
GeoGebra and Desmos 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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