Estimate T(3) using the values at t = 2 and t = 4.
Consider the following table giving temperature as a function of time.
Time, f Temperature, T (°C)
0.0 .......................... 0.172
1.0 .......................... 1.635
2.0 .......................... 6.492
3.0 .......................... 11.95
4.0 .......................... 20.24
The data follow the equation T(t) = t + t2, but there is some noise in each of the measurements, so that the values are not exactly on the curve. Estimate each of the following using the tangent line approximation and a secant line approximation. Which method do you think deals best with the noise?