Respuesta :
The relationship that explains the exponential relationship between the year and amount of energy used is: Option B: The amount of energy used decreases by different amount each year.
What is the rate of exponential function?
Rate of an exponential function is in terms of exponential function itself. It's not constant, and always changing. For example, the rate of [tex]y = e^x[/tex] with respect to x is [tex]y' = e^x[/tex] itself, which increases as x increases.
The given table is:
Year(Serial no.) Amount of energy used (kWh)
1 1,000,000
2 900,000
3 810,000
4 792,000
The differences between each consequent years of the amount of energy used is:
1000000 - 900000 = 100000
900000 - 810000 = 90000
810000 - 792000 = 18000
So, we see that the decrement is done by decreasing amount.
So rate of change wasn't constant but continuosly changing.
Thus, Option C is clearly wrong.
We see that 100,000 is 10% of 1,000,000
and 90,000 is 10% of next years amount 900,000
but 18,000 is not 10% of next years amount which is 810,000
Thus, Option A is wrong too.
Option B is correct in its statement, and so as option D because we don't see any immediate pattern in the decrement, except that the energy is just decreasing, so its unexpected.
The rate of exponentially related variables is not unexpected though.
So, its only Option B which is closest (among other options) to the intention of telling that the relation between the year and the amount of energy used is exponential, although it doesn't prove that the relationship is exponential. (because, suppose the function i take is [tex]y = x^2[/tex], then its rate with respect to x is [tex]y' = 2x[/tex] and this rate is also non-constant, but the function wasn't exponential).
Thus, the relationship that explains the exponential relationship between the year and amount of energy used is: Option B: The amount of energy used decreases by different amount each year.
Learn more about rates of exponential functions here:
https://brainly.com/question/1497850
