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# Math2413Homework#3 1. Findthebestmodelforeachofthefollowingsetsofdata.(Besuretoshowall work-i.youmaynotusetechnologytofindthemodelforyou.) x y 1 33 3...

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Math 2413 Homework #3 1. Find the best model for each of the following sets of data. (Be sure to show all work – i.e. you may not use technology to find the model for you.) x 1 3 6 10 15 y 33 39.93 53.15 77.81 125.32 X 1 3 6 10 15 Y 45.5 36.5 23 5 ‐17.5 2. Fill in the following table so that the data is quadratic. X 0 2 4 6 8 10 12 Y 36 28 22 3. Find the equation for the quadratic function that passes through the point (3,4) and reaches a maximum at (‐1,8). 4. The profit of a certain company is given by the function P ( x ) = 0.25 x 2 + 5 x + 15 , where x is the number of years since 1990 and P is measured in millions of dollars. a. Find and interpret P (8). b. Determine when the profit reached 25 million dollars. c. Determine when the profit reached a maximum. What was the maximum? d. Determine when the company broke even.
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Solution 1:
x
1
3
6
10
15 y
33
39.93
53.15
77.81
125.32 Difference
39.93 – 33 = 6.93
53.15 – 39.93 = 13.22
77.81 – 53.15 = 24.66
125.32 – 77.81 = 47.51 y = abx
At x = 1, y = 33
33 = ab1
a =...

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