Question: An electrical circuit is built with a variable resistor installed. For each of the following resistance values (measured in kiloohms, k), the power corresponding to

An electrical circuit is built with a variable resistor installed. For each of the following resistance values (measured in kiloohms, kΩ), the power corresponding to the load (measured in milliwatts, mW) is provided in the following table.

Resistance (kΩ)	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 scatterplot of the data using Endurance as the independent variable and Power as the dependent variable.

(b) Use your calculator (DesmosDesmos or Excel) 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 maximum predicted power that can be delivered to the load. What is the value of the corresponding resistance?

(d) Discuss the limitations of these models; in particular, discuss the final behavior of each.

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