## Exponential growth

### F(x)= a^x, |a| > 1 or F(x)= e^xD: all realsR: y > 0X-int.: noneY-int.: (0,1)

Exponential growth is a type of growth in which the rate of increase of a quantity is proportional to its current value. In other words, the larger the quantity, the more it grows at a given rate. This results in a rapid and sustained increase in the quantity over time.

The classic example of exponential growth is compound interest. When you invest money and earn interest, you not only earn interest on your initial investment but also on the interest that has accumulated. As a result, your investment grows faster and faster over time.

Another example of exponential growth is population growth. When a population grows exponentially, the number of individuals in the population increases rapidly over time, as each individual can reproduce and produce more offspring.

Exponential growth can also be observed in technological advancements, where new innovations build upon previous ones and accelerate progress at an ever-increasing rate.

However, exponential growth is not sustainable indefinitely. At some point, growth will reach a limit due to finite resources or other constraints. When this happens, growth may slow down or even decline. Understanding exponential growth is crucial for predicting future trends and planning for the future.

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