## Exponential Growth Function

### The exponential growth function is a mathematical model that describes the growth of a population or quantity that increases at a constant percentage rate over time

The exponential growth function is a mathematical model that describes the growth of a population or quantity that increases at a constant percentage rate over time. It is commonly written in the form of:

y = a * b^x

where:

– y represents the value of the quantity at a given time x.

– a represents the initial value or the value at x = 0.

– b represents the growth or decay factor. If b > 1, it represents exponential growth. If 0 < b < 1, it represents exponential decay.
To better understand this concept, let's consider an example.
Example: Suppose the initial value of a bacterial population is 100, and it doubles every hour. Write an exponential growth function to represent the population after x hours.
Solution: In this case, the initial value a = 100, and the growth factor b = 2 (since it doubles every hour). The exponential growth function can be written as:
y = 100 * 2^x
If we want to calculate the population after 3 hours, we substitute x = 3 into the equation:
y = 100 * 2^3
= 100 * 8 (since 2^3 = 8)
= 800
So, after 3 hours, the bacterial population would be 800.
Additionally, it's worth noting that the exponential growth function can also be expressed using the natural logarithm. It is given by:
y = a * e^(kx)
where e is the base of natural logarithm, and k is the constant growth rate. Both forms of the equation are equivalent and can be used interchangeably depending on the context or preference.
I hope this explanation helps you understand the concept of the exponential growth function. Let me know if you have any further questions!

## More Answers:

Understanding Asymptotes: Types and Determination for Math FunctionsUnderstanding Exponential Decay Models: Exploring the Concept and Calculation Behind the Decay Factor in Mathematics

Understanding Exponential Decay Functions: Explaining the Math Behind Decay and its Applications.