Question

what does it mean for a function to exhibit exponential growth?
exponential growth occurs when a quantity increases linearly over time.
exponential growth occurs when a quantity increases by a consistent percentage over equal time intervals, resulting in a rapid increase.
exponential growth occurs when a quantity remains constant over time.
exponential growth occurs when a quantity decreases by a consistent percentage over equal time intervals.

Explanation:

To determine the correct description of exponential growth, we recall the definition: Exponential growth occurs when a quantity increases by a consistent percentage over equal time intervals, leading to rapid growth (as the base of the exponential function is greater than 1, and the growth is multiplicative per interval). Let's analyze each option:

• First option: Says "increases linearly over time" – linear growth is additive (constant amount per time), not exponential. Eliminate.
• Second option: "occurs when a quantity increases by a consistent percentage over equal time intervals, resulting in a rapid increase" – matches the definition of exponential growth (multiplicative growth by a percentage, leading to accelerating growth).
• Third option: "a quantity remains constant over time" – this is no growth (constant), not exponential. Eliminate.
• Fourth option: "a quantity decreases by a consistent percentage over equal time intervals" – this is exponential decay, not growth. Eliminate.

Answer:

The correct option (assuming the second option is, for example, labeled as B, but based on the text): "Exponential growth occurs when a quantity increases by a consistent percentage over equal time intervals, resulting in a rapid increase."