To determine if the relationship between the year and the amount of energy used is exponential, we need to analyze how the amount of energy used changes year by year.
In an exponential relationship, the quantity decreases by a consistent percentage, rather than by a consistent amount. This means if we calculate the percentage decrease in energy usage from one year to the next, it would be relatively similar.
Let’s look at the energy usage from year to year:
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Year 1 to Year 2:
\[(1,000,000 - 900,000) / 1,000,000 = 10% \text{ decrease}\] -
Year 2 to Year 3:
\[(900,000 - 810,000) / 900,000 = 10% \text{ decrease}\] -
Year 3 to Year 4:
\[(810,000 - 792,000) / 810,000 \approx 2.22% \text{ decrease}\]
As you can observe, the percentage decrease is not consistent: the first two years saw a decrease of 10%, but the third year's decrease drops significantly to about 2.22%.
Because the reduction in energy does not occur at a consistent percentage rate year over year, the relationship cannot be described as exponential.
In conclusion, the relationship between the year and the amount of energy used does not follow an exponential function, as an exponential decay requires a consistent percentage decrease, which is not evident in this data. Instead, the data indicates variability in the rate of decrease.