Find a formula for the amount A of CO2 a car produces in terms of the number n of miles driven and the gas mileage G mi/gal of the car.
Is the amount A in direct proportion to n and G?
I believe so
To derive a formula for the amount of CO2 produced by a car in terms of the number of miles driven (n) and the gas mileage (G) of the car, we need to consider the following information:
1. The quantity of carbon dioxide (CO2) emitted by burning one gallon of gasoline.
2. The number of gallons of gasoline consumed to travel a certain number of miles.
Let's start by determining the amount of CO2 emitted per gallon of gasoline burned. According to the Environmental Protection Agency (EPA), the average amount of CO2 emitted per gallon of gasoline is approximately 8.887 kilograms (kg) or 19.57 pounds (lbs). However, we need to convert this value into the desired units.
1 pound (lb) is approximately equal to 0.4536 kilograms (kg).
Hence, the amount of CO2 emitted per gallon of gasoline can be expressed as follows:
CO2_per_gallon = 19.57 lbs * 0.4536 kg/lb ≈ 8.887 kg.
Next, we need to determine the number of gallons of gasoline consumed to travel a given number of miles (n) based on the gas mileage (G) of the car. The car's gas mileage represents the number of miles the car can travel on one gallon of gasoline. Therefore, we can express this relationship as:
gallons = n miles / G mi/gal.
Finally, to obtain the formula for the amount of CO2 emitted (A), we multiply the CO2 emitted per gallon by the number of gallons consumed:
A = CO2_per_gallon * gallons
= 8.887 kg * (n miles / G mi/gal).
Therefore, the formula for the amount of CO2 (A) produced by a car can be expressed as:
A = (8.887 kg * n miles) / G mi/gal.
This formula allows you to calculate the amount of CO2 produced by a car based on the number of miles driven (n) and the gas mileage (G) of the car.