Question

question 17
evaluating and solving rational functions
mr. ewald decides to make and sell left handed smoke shifters as a side business. the function below gives the average cost (in dollars) per smoke shifter when x smoke shifters are produced.
$a(x)=\frac{5x + 400}{x}$
use the function to answer the following questions.
determine ( a(11) ), and complete the sentence explaining the meaning of your answer. round your answer to the nearest cent.
the average cost to produce 11 left handed smoke shifters is $
how many smoke shifters must be produced in order to reduce the average cost to $13 each?
to reduce the average cost to produce each smoke shifter down to 13, smoke shifters must be produced.
give the equation of the horizontal asymptote of ( a(x) )
horizontal asymptote:
select a sentence to explain its significance in this situation.
select an answer
question help: 0

Explanation:

Step1: Calculate \( A(11) \)

Substitute \( x = 11 \) into \( A(x)=\frac{5x + 400}{x} \).

$$
LATEXBLOCK0
$$

Step2: Solve for \( x \) when \( A(x)=13 \)

Set \( \frac{5x + 400}{x}=13 \).
Multiply both sides by \( x \): \( 5x+400 = 13x \).
Subtract \( 5x \) from both sides: \( 400=13x - 5x \), so \( 8x = 400 \).
Divide both sides by \( 8 \): \( x=\frac{400}{8}=50 \).

Step3: Find the horizontal asymptote

For \( A(x)=\frac{5x + 400}{x}=5+\frac{400}{x} \), as \( x\to\pm\infty \), \( \frac{400}{x}\to0 \).
So the horizontal asymptote is \( y = 5 \).

Answer:

1. \( 41.36 \)
2. \( 50 \)
3. \( y = 5 \)