The density of water is well known to reach a maximum at a temperature slightly above freezing. The table shown below, from the Handbook of Chemistry and Physics (CRC Press, 2009), gives experimental data on the density of water in grams per cubic centimeter for five equally spaced temperatures from ~10°C to +30°C. Using this information, model the temperature-density dependence with an interpolating polynomial of degree 4.
Temperature (°C) Density (g/cm³)
10 998.15
20 999.87
30 999.73
Use the procedure for solving application problems that was discussed in Week 2. Define unknowns, derive equations, solve the linear system using MAPLE. Present your answer for the interpolating polynomial, plot the graph of the polynomial, and use the graph to estimate roughly the temperature at which the maximum in density of water occurs.