[Linear Least Squares] A simple linear least-squares-fit routine is at the end o

Question

[Linear Least Squares] A simple linear least-squares-fit routine is at the end of this project description. The program can be modified to include seemingly non-linear power equations and exponential equations as described in class on 3/20/12. Make sure you understand how the Matlab code uses matrices to produce the “least- squares-fit”. Verify the Matlab code is working by finding the coefficients for the exponential growth of bacteria per unit volume present in a culture after x hours (2-pts.);

The tabulated data is given below.

Hours (x)

0

1

2

3

4

5

6

Number (y)

32

47

65

92

132

190

275

Hours (x)

0

1

2

3

4

5

6

Number (y)

32

47

65

92

132

190

275

u ae

Explanation / Answer

We can get the value of coeficients by solving the equation , substitution (x,y) pair one at a time.

Equation: y = ae-bx

1) x=0 , y = 32

=> 32 = ae-b*0

=> 32 = ae0

=> 32 = a

2) x = 1 , y = 47

=> y = ae-bx

=> 47 = 32 * (2.71) -b*1

=> 47 = 32 * (2.71) -b

=> 47/32 = (2.71) -b

=> 1.46875 = (2.71) -b

taking log both sides;

.=> log(1.46875) = -b log (2.71)

=> log2.71(1.46875) = -b

=> -b = 0.3855882695021

=> b = -0.3855882695021

hence, a = 32

b = -0.3855882695021

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