Understanding Exponential Growth Function: Definition, Formula, and Examples

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!

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