An electric circuit is built with a variable resistor installed. For each of the following resistance values (measured in kilo-ohms, k), the corresponding power to the load (measured in milliwatts, mW) is given in the table below.

Resistance: (k) 1.012, 2.199, 3.275, 4.676, 6.805, 9.975

Power: (mW) 1.063, 1.496, 1.610, 1.613, 1.505, 1.314

(a) Make a scatter diagram of the data using the Resistance as the independent variable and Power as the dependent variable.

(b) Use your calculator to find quadratic (2nd degree), cubic (3rd degree) and quartic (4th degree) regression models for the data and judge the reasonableness of each.

(c) For each of the models found above, find the predicted maximum power that can be delivered to the load. What is the corresponding resistance value?

(d) Discuss with your classmates the limitations of these models - in particular, discuss the end behavior of each.