24.00 And sold it for 34.00 What is the percent of increase rounded to the nearest tenth
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Answer:
, see the graph attached for a visual reference.
Step-by-step explanation:
Vertical asymptotes are only present in rational functions where the parent function has a vertical asymptote at the line
and a horizontal asymptote at the line
. Because the vertical asymptote has to be
, the denominator must be x-7 in order for the denominator to equal 0. For the horizontal asymptote to be
, then 3 must be subtracted from the rational function. Therefore, the function that has these asymptotes is
.
Any function to determine profit is revenue - cost.
If the number of mattresses made is x, then the revenue made per mattress is 365x.
Under the same assumption, the cost per mattress is 254x + 9100, adding the setup costs to the cost per mattress.
Thus, the function is
. We can simplify this function.
First, lets expand the negative (the same as multiplying each value by -1).
Next, we'll combine like terms.
Therefore, the function for profit is.
Continuing, we need to determine how many mattresses the company needs to break even. Breaking even means there is no profit, but also no loss. Otherwise, they make 0 total. So, we can set the function we just found to 0 and solve for x.
Set the function to 0.
Add 9100 to both sides.
Divide both sides by 111.
Rounding this number up, it would take 82 mattresses to break even.
If the number of mattresses made is x, then the revenue made per mattress is 365x.
Under the same assumption, the cost per mattress is 254x + 9100, adding the setup costs to the cost per mattress.
Thus, the function is
First, lets expand the negative (the same as multiplying each value by -1).
Next, we'll combine like terms.
Therefore, the function for profit is
Continuing, we need to determine how many mattresses the company needs to break even. Breaking even means there is no profit, but also no loss. Otherwise, they make 0 total. So, we can set the function we just found to 0 and solve for x.
Set the function to 0.
Add 9100 to both sides.
Divide both sides by 111.
Rounding this number up, it would take 82 mattresses to break even.