Which description best defines Exponential Growth?

Which description best defines Exponential Growth?

• A. A quantity increases linearly with time.
• B. A quantity decreases towards zero.
• C. A quantity remains constant.
• D. Growth whose rate becomes ever more rapid in proportion to the growing total number or size.

Answer: (D)

Exponential growth occurs when the growth rate is proportional to the current size. This means that as the quantity grows, the amount it increases in a given period grows as well, so the total growth accelerates over time. The description that matches this idea is the one that says the growth rate becomes ever more rapid in proportion to the growing total number or size. For contrast, linear growth adds a fixed amount each period and doesn’t accelerate, decay toward zero describes shrinking, and a constant quantity doesn’t change at all. A familiar example is a population that doubles or a quantity that follows N(t) = N0 e^{kt} with k > 0; as N grows, the increments in N over equal time intervals become larger.

Exponential growth occurs when the growth rate is proportional to the current size. This means that as the quantity grows, the amount it increases in a given period grows as well, so the total growth accelerates over time. The description that matches this idea is the one that says the growth rate becomes ever more rapid in proportion to the growing total number or size.

For contrast, linear growth adds a fixed amount each period and doesn’t accelerate, decay toward zero describes shrinking, and a constant quantity doesn’t change at all. A familiar example is a population that doubles or a quantity that follows N(t) = N0 e^{kt} with k > 0; as N grows, the increments in N over equal time intervals become larger.