Problem 2 (5 points) : Interpolation

The table below lists values for dissolved oxygen concentration in water (with a chloride concentration of 20 g/L) as a function of temperature.

T (C)	0	5	10	15	20	25	30
Dissolved oxygen (mg/L)	11.4	10.3	8.96	8.08	7.35	6.73	6.20

We ultimately wish to estimate the dissolved oxygen concentration at a temperature of 2.1 C.

1. Interpolate the data in two ways:

   1. using a polynomial that goes through all the data points
   2. using a polynomial of the appropriate degree that goes through the first 3 data points

   Display the coefficients of each interpolating polynomial.

2. Plot the data points and the interpolating polynomials on a single figure. Use black diamonds to represent the data points. Plot the polynomial through all the data points over the range T = 0 to 30 C and as a blue dotted line. Plot the polynomial through just the first 3 data points over the range T = 0 to 10 C and as a dashed red line.

3. Estimate the dissolved oxygen concentration at a temperature of 2.1 C in three ways:

   1. using your polynomial interpolation through all the data points
   2. using your polynomial interpolation through the first 3 data points
   3. using a spline interpolation