Gas or Electric? Thinking Algebraically About Car Costs, Emissions and Trade-offs

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Gas or Electric? Thinking Algebraically About Car Costs, Emissions and Trade-offs

Provide a written response: At approximately what year does the Camry start to become more expensive to own than the Tesla? Use evidence from both the table and the graph to support your answer.

Answer: At about eight years of ownership, the Camry surpasses the expenses of the Tesla in the table of values. In addition, the lines in the graph representing our models “cross” at Year 8 — at this point, the Camry’s higher rate of cost per year finally “catches up” with the Tesla (which had a higher starting cost).

In addition to costs, we can also model the total greenhouse gas emissions associated with each vehicle over time. Although Tesla is better for the climate over time, the Camry puts out less emissions during its production. Answer the next questions to explore the emissions trade-offs for these vehicles:

1. The upfront vehicle and battery production for the Tesla creates emissions in the amount of 11,074 kg CO2-eq (this unit of measurement means “emissions equivalent to the global warming potential of 11,074 kilograms of CO2”). The power sources that create electricity to charge the battery expend about 1,368 kg CO2-eq per year. Create a mathematical model to determine total emissions (in kg CO2-eq) for the Tesla:

Answer: Where x represents the number of years you’ve owned the car:

Tesla: Total Emissions =1368x+11074

2. The upfront vehicle production for the Camry creates 7,402 kg CO2-eq of emissions. The production of fuel and burning of fuel needed to drive the car produces 4,525 kg CO2-eq per year. Create a mathematical model for the Camry:

Answer: Where x represents the number of years you’ve owned the car:

Camry: Total Emissions=4525x+7402

3. Approximately how many years will it take for the Camry to produce more total emissions than the Tesla? Show your work using a table of values and a graphical sketch.

Answer: The Tesla becomes more emissions-efficient shortly after the first year of ownership. By Year 2, according to the table, the Tesla has lower overall emissions. In the graph, we see the lines “cross” shortly after Year 1, as the Tesla begins to have lower total emissions because of its lower rate of emissions per year. Hands down, the Tesla is the more environmentally-friendly option, and it grows more environmentally friendly with each passing year.