### Curve Fitting

```Curve Fitting
Learning Objective: to fit data to non-linear functions and make predictions
Warm-up (IN)
1.
Find all the critical points for f  x   2x4  3x2  5
2. Solve by factoring 2 x2  5x  12  0
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.
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
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.
Ex 3 – The data below represents monthly cost of
manufacturing bicycles, C, and the number of bicycles
produced, x.
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
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?
Out – none
Summary – describe the difference between a linear,
quadratic and cubic graph
HW – curve fitting
wksht
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