The amount at a given time can be calculated by multiplying the previous amount by a value less than 1, which represents exponential decay. Hence, option B is the right choice.
What does linear function mean?
A quantity grows (or depreciates) linearly if it increases (or decreases) by the same amount per unit of time.
What does exponential function mean?
A quantity grows (or depreciates) exponentially if the increase (or decrease) in the amount is a multiple of the previous amount.
How to solve the question?
In the question, we are asked to identify the option that best describes an exponential decay.
We assess each option and try to identify the exponential decay among them.
- A. The amount at a given time can be calculated by multiplying the previous amount by a value greater than 1: This is an exponential function as it is multiplied by the previous amount, but it shows exponential growth as the quantity multiplied is greater than 1.
- B. The amount at a given time can be calculated by multiplying the previous amount by a value less than 1: This is an exponential function as it is multiplied by the previous amount, and it shows exponential decay as the quantity multiplied is less than 1.
- C. The amount at a given time can be calculated by adding an amount to the previous amount: This is a linear function as a fixed quantity is added.
- D. The amount at a given time can be calculated by subtracting an amount from the previous amount: This is a linear function as a fixed quantity is subtracted.
Therefore, the amount at a given time can be calculated by multiplying the previous amount by a value less than 1, which represents exponential decay. Hence, option B is the right choice.
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