Exponential growth is the process by which quantity increases over time, proportional to the quantity itself. It is described as a function where an exponentially growing quantity is an exponential function of time. Exponential growth creates a curve of an exponential function that increases more and more over time. This pattern is seen when populations double or triples, and the data can be expected to grow exponentially. Exponential growth produces an upward curve on a graph when plotted. The opposite of exponential growth is exponential decay, where the data shrinks rather than grows.
What is Exponential Growth and How Does it Work?
Exponential growth is a process in which a quantity increases over time. This means that the rate of change of the quantity after a certain amount of time is proportional to the quantity itself. As a function, an exponentially growing quantity is an exponential function of time, where the variable representing time is the exponent. This is different from other types of growth, such as quadratic growth, where the quantity increases at a slower rate.
What are Examples of Exponential Growth?
One example of exponential growth is population growth. Let’s say that a population of mice increases exponentially by a factor of 2 each year, starting with 2 in the first year. In the second year, there would be 4 mice, in the third year there would be 8, and so on. Another example is the growth of a bank account with compound interest. The interest earned each year is added to the account balance, creating an upward curve on a graph.
How Does Exponential Growth Look on a Graph?
When plotted on a graph, exponential growth produces a curve that appears to increase more and more over time. The curve starts out shallow, then becomes steeper as the quantity increases. This upward curve represents the growth of the quantity over time. The curve can be used to predict future growth, such as the growth of a population, based on its past growth rate.
What is Exponential Decay?
Exponential decay is the opposite of exponential growth. It occurs when a quantity shrinks over time instead of growing. This means that the rate of change of the quantity after a certain amount of time is proportional to the quantity itself, but with a negative sign. Exponential decay can be seen in radioactive decay, where the amount of a radioactive substance decreases over time.
In Overall, exponential growth is a process in which a quantity increases over time in an exponential way. It can be seen in population growth, compound interest, and other examples. Exponential growth produces an upward curve on a graph, which can be used to predict future growth. On the other hand, exponential decay is the opposite of exponential growth and occurs when a quantity decreases over time.