a) To approximate the data \(\displaystyle{T}={87.97}\ +\ {3496}\ \text{p}\ +\ {7.91}\ \sqrt{{{p}}}\) and the table provided in the question shown below. \begin{array}{|c|c|} \hline Pressure,\ p & Temperature \\ \hline 5 & 162.24^{\circ} \\ \hline 10 & 193.21^{\circ}\\ \hline 14.696\ (1\ atm) & 212.00^{\circ}\\ \hline 20 & 227.96^{\circ}\\ \hline 30 & 250.33^{\circ}\\ \hline 40 & 267.25^{\circ}\\ \hline 60 & 292.71^{\circ}\\ \hline 80 & 312.03^{\circ}\\ \hline 100 & 327.81^{\circ}\\ \hline \end{array}ZSK Graph: Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press Y= button.

Step 3: Enter the data \(\displaystyle{87.97}\ +\ {3496}\ \text{In}\ {p}\ +\ {7.91}\ \sqrt{{{p}}}\) which is required to graph. Step 4: Press GRAPH button to graph the function. The graph is obtained as: Interpretation: From the graph it is observed that graph shows the curve. b) Calculate: From the above graph the pressure required is 67.29 pounds per square inch. c) Calculation: \(\displaystyle{T}={87.97}\ +\ {3496}\ \text{In}\ {p}\ +\ {7.91}\ \sqrt{{{p}}}\)

\(\displaystyle{T}{\left({74}\right)}={87.97}\ +\ {3496}\ \text{In}{\left({74}\right)}\ +\ {7.91}\ \sqrt{{{74}}}\)

\(\displaystyle{T}{\left({74}\right)}={306.4845}\)