Numerical Method20775 marksNumerical: exponential curve fittingNon-linear Regression by fitting Exponential and Polynomial
Fit the curve y = aebx through the following data points. | x | 1 | 2 | 3 | 4 | |---|---|---|---|---| | y | 1.65 | 2.70 | 4.50 | 7.35 |
Fit the curve $y = ae^{bx}$ through the following data points.
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 1.65 | 2.70 | 4.50 | 7.35 |
[5]
$x$ 1 2 3 4 ------------------------- $y$ 1.65 2.70 4.50 7.35 $n = 4$ Taking natural logarithm: $$\ln y = \ln a + bx$$ Let $Y = \ln y$, $A = \ln a$, $B = b$: $$Y = A + Bx$$ $x$ $y$ $Y=\ln y$ $x^2$ $xY$ -------------------------- 1 1.65 0.50078 1 0.50078 2 2.70 0.99325 4 1.98650 3 4.50 1.50408 9 4...