What is the formula used to express exponential growth?

The formula that expresses exponential growth is represented by the equation P = P_0 * (2^n). In this equation, P denotes the future population or quantity, P_0 represents the initial population or quantity, and n is the number of time intervals that have passed. The factor of (2^n) signifies that the population or quantity doubles with each time interval. This is a classical representation of exponential growth, particularly in scenarios where the growth rate is constant, leading to a rapid increase over time.

In contrast, the other options do not encapsulate the principle of exponential growth. The additive formula P = P_0 + n indicates linear growth, where the quantity increases by a constant amount n, rather than growing exponentially. The formula P = n^2 suggests polynomial growth, where the growth rate accelerates with the increase in n, but it does not reflect the continuous compounding nature seen in exponential growth. Lastly, P = P_0 / (2^n) represents exponential decay rather than growth, indicating a reduction in quantity as n increases. Thus, the chosen formula accurately captures the essential characteristics of exponential growth.