Numerical Methods20785 marksNumerical: Curve fitting exponentialExponential curve fitting
The temperature of a metal strip was measured at various time intervals during heating and the values are given in the table below. If the relation between the time 't' and temperature 'T' is of the form: T = bet/4 + a. Estimate the temperature at t = 6 minute. | Time ('t' min) | 1 | 2 | 3 | 4 | |--
The temperature of a metal strip was measured at various time intervals during heating and the values are given in the table below. If the relation between the time 't' and temperature 'T' is of the form: $T = be^{t/4} + a$. Estimate the temperature at t = 6 minute.
| Time ('t' min) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Temp ('T' °C) | 70 | 83 | 100 | 124 |
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Relation: $T = be^{t/4} + a$ t (min) 1 2 3 4 --------------- T (°C) 70 83 100 124 Estimate: T at t = 6. Substitute $u = e^{t/4}$, giving the linear form $T = a + bu$. Compute u values: t T $u = e^{t/4}$ --------- 1 70 $e^{0.25} = 1.28403$ 2 83 $e^{0.50} = 1.64872$ 3 100 $e^{0.75} = 2.11700$ 4 124...