The revenue R, generated by selling a particular product at a price p is modeled by a quadratic polynomial. In the table below, three prices and their corresponding revenue (in millions of dollars) are given.
| p | 0.50 | 0.45 | 0.60 |
| R | 7 | 6.345 | 8.28 |
a. Using polynomial interpolation, find the quadratic function for the revenue.
b. Calculate the revenue when the product is sold at a price of $0.52
The stopping distance d (in feet), under the best of conditions, was measured for three vehicles traveling at the given speeds x (in miles per hour).
a.Find a quadratic equation that gives the stopping distance as a function of speed.
| x | 25 | 50 | 100 |
| d | 55 | 165 | 550 |
b. Calculate the stopping distance for a vehicle travelling at 35 mph.
| p | 0.50 | 0.45 | 0.60 | 0.48 |
| R | 7 | 6.345 | 8.28 | 6.6 |
a. Use the method of least squares to find a quadratic that best fits the new data.
b. Again, calculate the revenue when the product is sold at a price of $0.52.
| x | 25 | 50 | 100 | 40 |
| d | 55 | 165 | 550 | 110 |
a. Use the method of least squares to find a quadratic polynomial that best fits these points.
b. Calculate the stopping distance for a vehicle travelling at 35 mph.