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Unformatted text preview: ) / ( a 2 2 + b 2 2 )] 1 / 2 or its inverse, as obtained in part (iii) . Solved Examples (see also Homework Problem 16) S 17.1 ( P 2.29 in textbook). Five measurements x i taken at times t i are shown below. t i 0.1 0.2 0.3 0.4 0.5 x i 2.88 3.48 4.29 5.00 6.25 It is believed that the data follow an exponential law of the form x ( t ) = ae bt or equivalently, ln x ( t ) = ln a + bt Determine the values of a and b in the least squares approximation of the vector [ s i ] = [ln x i ] by the vector [ln a + bt i ] (where i = 1 ,..., 5). S 17.2 ( P 2.30 in textbook). Five measurements x i taken at times t i are shown below. t i 10 20 30 40 50 x i 14.0 20.9 26.7 32.2 36.8 It is believed that the data obey a power law of the form x ( t ) = at r or equivalently, ln x ( t ) = ln a + r ln t Determine the values of a and r in the least squares approximation of the vector [ s i ] = [ln x i ] by the vector [ln a + r ln t i ] (where i = 1 ,..., 5)....
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 Spring '08
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