Which formula represents exponential growth?

The formula that represents exponential growth is y = a(1 + r)^t. In this formula, 'a' represents the initial amount or value, 'r' is the growth rate (expressed as a decimal), and 't' is the time period. As time progresses, the value of y increases exponentially due to the compounding effect of the growth rate.

This occurs because each time period, the increase is not just added to the initial amount, but also to the previously gained value. This is a characteristic feature of exponential growth, where the quantity grows by a percentage of the current amount rather than a fixed absolute amount, leading to rapid increases over time.

The other choices represent different types of growth or functions. The formula y = a(1 - r)^t indicates exponential decay rather than growth, while y = a + rt represents a linear relationship where the value increases by a constant amount, not at an increasing rate. Finally, y = ab^t is also a representation of exponential growth but in a slightly different form, where 'b' is the base of the exponential function and must be greater than 1 to indicate growth.

Thus, option B clearly indicates exponential growth with the correct structure of growth factor and