Answer:
- The equation that models the revenue is r = -100|x -700| +70000
- The revenue will be $55,000 for 500 units and 900 units
Step-by-step explanation:
This problem gives no clue as to Mike's revenue with zero phones sold. We can assume it is zero. In that case, only one equation evaluates to r = 0 for x = 0: the first one.
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If you have been paying attention to what function transformations do, you see that the absolute value function f(x)=|x| has been reflected across the x-axis and scaled by a factor of 100: f1(x) = -100|x|, then translated so its vertex is at (x, r) = (700, 70000): r = -100|x -700| +70000.
Among other things, this tells you the function is symmetric about its vertex at x=700. That is, the numbers of phones sold at which revenue is the same will be symmetric about x=700. The numbers 500 and 900 match that description. The numbers 900 and 1200 are both above 700, where revenue is declining, so their revenue values cannot be the same.
