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1)The acceleration of certain objects is studied in an experimental test track for automobiles. The distance traveled by an object L is measured as a function of time t to yield the following:

t(s)

0.1

0.2

0.5

1.0

1.5

1.8

2.0

3.0

L(m)

0.26

0.55

1.56

3.90

7.41

10.28

12.6

30.9

Obtain a best fit to this data, considering first-,second, and third-order polynomials. Using these polynomials, calculate the values of the dependent variable L at the time intervals employed for the given data to evaluate the accuracy of the polynomial representations. Discuss the results obtained.
 
2)The temperature T of a small copper sphere cooling in air is measured as a function of time t to yield the following:

 

t(s)

0.2

0.6

1.0

1.8

2.0

3.0

5.0

6,0

8.0

T(C)

146.0

129.5

114.8

90.3

85.1

63.0

34.6

25.6

14.1

An exponential temperature decrease is expected from theoretical considerations. Using linear regression, obtain the exponent c and the constant C, where 
T=Ce^(-ct) represents the variation. Also, solve this problem using the polyfit function in MATLAB.
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