Which statement best describes Exponential Growth?

• A. Growth whose rate becomes ever more rapid in proportion to the growing total number or size.
• B. Growth at a constant amount per unit time.
• C. Growth that eventually stops.
• D. Growth that depends on the square of the input.

Answer: (A)

Exponential growth means the amount you gain each period is proportional to what you already have, so the growth rate itself gets larger as the quantity grows. The statement that matches this idea exactly is that the growth rate becomes ever more rapid in proportion to the growing total. In mathematical terms, if the quantity is N, the change satisfies dN/dt = kN, which leads to N(t) = N0 e^{kt}: the percent growth per unit time stays the same, but the absolute increase rises as N grows, producing a rapid, accelerating rise.

Consider other patterns: growth by the same fixed amount each period is linear, not exponential. Growth that eventually stops describes a leveling off or a limit, not ongoing acceleration. Growth depending on the square of the input is quadratic, which accelerates differently and, for large values, is outpaced by exponential growth.