Understanding Exponential Growth Functions | Definition, Formula, and Applications

Exponential Growth Function

An exponential growth function is a mathematical equation that describes a situation where a quantity increases at an ever-increasing rate over time

An exponential growth function is a mathematical equation that describes a situation where a quantity increases at an ever-increasing rate over time. It is characterized by the constant ratio between the rate of increase and the current quantity.

The general form of an exponential growth function is expressed as:

y = a * b^x

where:
– y represents the final quantity or value
– a is the initial quantity or value (often called the initial condition or the value at x = 0)
– b is the base, which is a positive constant greater than 1 that determines the rate of growth
– x is the input or independent variable, usually representing time or some other parameter

In an exponential growth function, as the value of x increases, the quantity y grows at an increasing rate, with the rate of growth determined by the value of b. As x approaches infinity, the quantity y approaches infinity as well.

For example, let’s consider the growth of a population. Suppose you have a population of 100 bacteria initially (a = 100) and the bacteria double every hour (b = 2), then the growth function can be represented as:

P(t) = 100 * 2^t

where P(t) is the population size at time t.

If we substitute t = 1 into the equation, we get:

P(1) = 100 * 2^1 = 200

This means that after one hour, the population would have doubled from the initial 100 to 200 bacteria. Similarly, after two hours, the population would be:

P(2) = 100 * 2^2 = 400

and after three hours:

P(3) = 100 * 2^3 = 800

As you can see, the population grows at an ever-increasing rate with time due to exponential growth.

Exponential growth functions have many applications in various fields, including finance, biology, physics, and computer science. They can be used to model population growth, compound interest, radioactive decay, viral spread, and more.

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