Question

using the model of the city of charleston, we can see how many kilowatt - hours (kwh) of power are generated from different amounts of ethanol. the data is summarized in the table.
ethanol (gal)\t100\t200\t300\t400\t500\t600
energy (kwh)\t2200\t4400\t6600\t8800\t11000\t13200
discuss & write: how much energy, in kwh, is generated by 1 gallon of ethanol? explain or show your thinking.
discuss & write: in the ethanol - energy function, which quantity is the input? which quantity is the output? explain how you know.

Explanation:

Step1: Identify input - output

In a function, the input is what we start with and the output is the result. Looking at the table of ethanol (gal) and energy (kWh), the amount of ethanol is what we control or start with, and the energy generated is the result.

Step2: Determine energy per gallon

To find out how much energy is generated by 1 gallon of ethanol, we can take any pair of values from the table and divide the energy (kWh) by the amount of ethanol (gal). For example, if we take the pair where ethanol is 100 gal and energy is 2200 kWh.
Let $E$ be the energy and $V$ be the volume of ethanol. The formula for energy per gallon $e$ is $e=\frac{E}{V}$.
Substituting $E = 2200$ kWh and $V=100$ gal, we get $e=\frac{2200}{100}=22$ kWh/gal.

Answer:

22 kWh of energy is generated by 1 gallon of ethanol. The input in the ethanol - energy function is the amount of ethanol (in gallons), and the output is the amount of energy (in kWh) generated.