Exponential growth is the increase in number or size at a constantly growing rate. In exponential growth, a population’s per individual growth rate stays the same regardless of the population size, making it grow faster and faster until it becomes large. Exponential growth is a pattern of data that shows greater increases with passing time creating the curve of an exponential function.

Opening Problem

• Suppose there are 15 fishes in an aquarium. After one year they had increased to 135.
• If the fishes are growing exponentially, then:
• At the end of five years, how many fishes will there be in the aquarium?
• At the end of ten years, how many fishes will there be in the aquarium?
• How many years will it take for the number of fishes to be double?

What is exponential growth? If something is increasing or growing rapidly as a result of a constant rate of growth applied to it, then it is experiencing exponential growth.

Exponential growth can be modeled with the exponential function

y = f (x) = ab^x, where a > 1 and b > 1.

In the equation y = f (x) = ab^x, x is the exponent, a is the starting amount when x = 0 and b is the base, rate or growth factor and it is a constant and it is greater than 1.