In a general exponential growth model with initial amount P0 and growth factor b per period, the amount after m periods is:

In a general exponential growth model with initial amount P0 and growth factor b per period, the amount after m periods is:

• A. P0 + bm
• B. P0 m^b
• C. b^(P0 m)
• D. P0 b^m

Answer: (D)

Exponential growth means you multiply the starting amount by the growth factor each period. After m periods, you’ve applied that multiplication m times, so the amount is the initial amount times the factor raised to the m-th power: P0 × b^m. This reflects compounding, where each period builds on the previous amount. The other forms don’t model this process: adding bm would be linear growth, m^b or b^(P0 m) rearranges the variables and exponents in ways that don’t represent compounding from the initial amount.

Exponential growth means you multiply the starting amount by the growth factor each period. After m periods, you’ve applied that multiplication m times, so the amount is the initial amount times the factor raised to the m-th power: P0 × b^m. This reflects compounding, where each period builds on the previous amount.

The other forms don’t model this process: adding bm would be linear growth, m^b or b^(P0 m) rearranges the variables and exponents in ways that don’t represent compounding from the initial amount.