Question

1. constructing the equation for the relationship between corn and ethanol

ethanol (e) gallons 0.5 1 1.5 2 2.5
corn (c) lbs 1 10 20 30 40 50
discuss & write: how many gallons of ethanol is produced by 1 pound of corn? explain how you found this value using the graph and/or the table and record your answer in the table.
discuss & write: write an equation to determine the number of gallons of ethanol, e, produced from c gallons of corn.
discuss & write: use your equation to determine the number of gallons of ethanol produced from 75 pounds of corn. show your work.

Explanation:

Step1: Find the unit - rate

From the table, when \(c = 1\) pound of corn, \(E=0.05\) gallons of ethanol. So the amount of ethanol produced per pound of corn is \(0.05\) gallons per pound.

Step2: Write the equation

The relationship between the amount of ethanol \(E\) (in gallons) and the amount of corn \(c\) (in pounds) is a linear relationship of the form \(E = mc\), where \(m\) is the slope (unit - rate). Since \(m = 0.05\), the equation is \(E=0.05c\).

Step3: Find ethanol from \(c\) gallons of corn

If \(c\) is the number of pounds of corn, using the equation \(E = 0.05c\), we can find the amount of ethanol.

Step4: Find ethanol from 75 pounds of corn

Substitute \(c = 75\) into the equation \(E=0.05c\). Then \(E=0.05\times75 = 3.75\) gallons.

Answer:

The equation is \(E = 0.05c\). The amount of ethanol produced from 75 pounds of corn is 3.75 gallons.