Curve FittingLearning Objective: to fit data to non-linear functions and make predictions

Warm-up (IN)

1. Find all the critical points for

2. Solve by factoring

4 22 3 5f x x x

22 5 12 0x x

Notes!

Ex 1 – Brian wanted to determine the relation that might exist between speed and miles per gallon of an automobile. Let x be the average speed of a car on the highway measured in miles per hour and let y represent the miles per gallon of the automobile. The following data are collected:

a. Find the regression equation for the data.

b. Explain what the slope means.

c. Predict the miles per gallon of a car traveling 61 miles per hour.

Ex 2 – The data below represents the average fuel consumption, C, by cars (in billions of gallons) for the years, t, 1980-1993.

a. Find the regression equation for the data.

b. Determine the year in which average fuel consumption was lowest.

c. Predict the average fuel consumption for 1994.

t ‘80 ‘81 ‘82 ‘83 ‘84 ‘85 ‘86 ‘87 ‘88 ‘89 ‘90 ‘91 ‘92 ‘93

C 71.9 71.0 70.1 69.9 68.7 69.3 71.4 70.6 71.9 72.7 72.0 70.7 73.9 75.1

Ex 3 – The data below represents monthly cost of manufacturing bicycles, C, and the number of bicycles produced, x.

a. Find the regression equation for the data.

b. Determine the cost of manufacturing 230 bicycles.

c. How many bicycles can be produced if costs are equal to $55,000?

x 0 100 150 180 205 220 225 240 265 280 300

C 10,000 30,000 39,000 43,950 47,825 50,075 50,850 53,325 57,750 60,675 65,075

HW – curve fitting wksht

Out – none

Summary – describe the difference between a linear, quadratic and cubic graph Don’t forget

about POW!!