Two software companies are developing new android apps. The average profit per x hundred downloads earned by each company can be modelled by the rational functions below, where x > or equal to 0.
Trance Media: G(x)=80x+150/x
Ellen's incorporated: B(x)=35x+600/x
How many downloads are required for the profit earned by Trance Media to be grater than the profit earned by Elena incorporated? Provide full algebraical solution, including a sign chart.
angelina/Aidan/andre/angelina -- please use the same name for your posts.
Very weird!
Sorry me and my friends were working together so everyone was asking question with their names.
Could someone please help me with this!
To find the number of downloads required for Trance Media's profit to be greater than Ellen's Incorporated, we need to set up an inequality and solve for x. Here's how to do it:
1. Set up the inequality:
We want the profit earned by Trance Media (G(x)) to be greater than the profit earned by Ellen's Incorporated (B(x)).
G(x) > B(x)
Instead of comparing the actual rational functions, we can compare their numerators since their denominators are the same.
80x + 150/x > 35x + 600/x
2. Get rid of the fractions:
To get rid of the fractions, multiply both sides of the inequality by the common denominator (x).
(x) * (80x + 150/x) > (x) * (35x + 600/x)
80x^2 + 150 > 35x^2 + 600
3. Simplify the equation:
Rearrange the equation to bring all terms to one side.
80x^2 - 35x^2 + 150 - 600 > 0
45x^2 - 450 > 0
4. Set up the sign chart:
A sign chart helps us to determine the values of x that satisfy the inequality. We need to find the values where the expression is positive and negative.
x ------+-------+------
-∞ 0 ∞
5. Test the intervals:
Pick a value from each interval and substitute it into the simplified expression.
For x < 0: Choose x = -1
45(-1)^2 - 450 > 0
45 - 450 > 0
-405 > 0 (False)
For 0 < x < ∞: Choose x = 1
45(1)^2 - 450 > 0
45 - 450 > 0
-405 > 0 (False)
6. Determine the solution:
Since the simplified expression is negative for all values of x, there are no solutions for this inequality. This means that Trance Media's profit will never be greater than Ellen's Incorporated profit based on the given rational functions.
In other words, Trance Media will not surpass Ellen's Incorporated in profit for any number of downloads.