Fit the exponential curve y = aebx for (1,15), (2,22), (3,33), (4,48), | Numerical Methods 2082

Numerical Methods20825 marksNumerical: least squares curve fittingExponential curve fitting

Fit the exponential curve $y = ae^{bx}$ for (1,15), (2,22), (3,33), (4,48), (5,70) using least square method. [5]

Points: $(1,15), (2,22), (3,33), (4,48), (5,70)$ , with $n = 5$ . Taking natural log: $\ln y = \ln a + bx$ Let $Y = \ln y$ , $A = \ln a$ . Then $Y = A + bx$ (linear). Normal equations: $\sum Y = nA + b\sum x$ $\sum xY = A\sum x + b\sum x^2$ $x$ $y$ $Y = \ln y$ $x^2$ $xY$ --------------- 1 15 2....

Points: $(1,15), (2,22), (3,33), (4,48), (5,70)$, with $n = 5$. Taking natural log: $$\ln y = \ln a + bx$$ Let $Y = \ln y$, $A = \ln a$. Then $Y = A + bx$ (linear). Normal equations: $$\sum Y = nA + b\sum x$$ $$\sum xY = A\sum x + b\sum x^2$$ $x$ $y$ $Y = \ln y$ $x^2$ $xY$ --------------- 1 15 2....

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Fit the exponential curve y = aebx for (1,15), (2,22), (3,33), (4,48), (5,70) using least square method.