Question

choose the correct answer below.

a. linear growth occurs when a quantity grows by the same absolute amount in each unit of time, and exponential growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time.
b. linear growth occurs when a quantity grows by different, but proportional amounts, in each unit of time, and exponential growth occurs when a quantity grows by random amounts in each unit of time.
c. linear growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time, and exponential growth occurs when a quantity grows by the same absolute amount in each unit of time.
d. linear growth occurs when a quantity grows by random amounts in each unit of time, and exponential growth occurs when a quantity grows by different, but proportional amounts, in each unit of time.

Explanation:

Define linear growth

Linear growth occurs when a quantity increases by a constant constant absolute amount in each equal interval of time.

Define exponential growth

Exponential growth occurs when a quantity increases by a constant relative amount, meaning it grows by a constant percentage in each equal interval of time.

Evaluate option A

Option A states that linear growth occurs when a quantity grows by the same absolute amount in each unit of time, and exponential growth occurs when a quantity grows by the same relative amount (by the same percentage) in each unit of time. This matches our definitions perfectly.

Evaluate other options

• Option B incorrectly describes linear growth as growing by different but proportional amounts, and exponential growth as growing by random amounts.
• Option C reverses the definitions, stating linear growth is relative (percentage) and exponential growth is absolute.
• Option D incorrectly describes linear growth as growing by random amounts, and exponential growth as growing by different but proportional amounts.

Answer:

• (A) Linear growth occurs when a quantity grows by the same absolute amount in each unit of time, and exponential growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time. (Correct answer)
• (B) Linear growth occurs when a quantity grows by different, but proportional amounts, in each unit of time, and exponential growth occurs when a quantity grows by random amounts in each unit of time.
• (C) Linear growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time, and exponential growth occurs when a quantity grows by the same absolute amount in each unit of time.
• (D) Linear growth occurs when a quantity grows by random amounts in each unit of time, and exponential growth occurs when a quantity grows by different, but proportional amounts, in each unit of time.