Mathematics concepts can be difficult to understand if you don’t pay attention when taking the lessons.
Geometric and Exponential growth are related concepts that might be easily interchanged but are distinct and have elaborate differences and similarities.
So, what are the most significant differences between geometric vs. exponential growth?
Geometric growth is discrete as it applies a fixed ratio, while exponential growth is continuous. For instance, you can multiply a fixed number to x with geometric growth and raise a fixed number to the x with exponential growth.
Here are the geometric vs. exponential growth similarities and differences
What Are the Differences between Geometric and Exponential Sequences?
The geometric growth is discrete, meaning it can multiply a fixed number to X, while exponential growth is continuous, which means it can raise a fixed number to X.
For instance, on a graph, geometric growth variables will be represented by dots as they are not continuous but discrete.
On the other hand, you will represent the exponential growth variables with a straight line or curve as the variables are continuous.
Geometric growth lists non-zero values that can be multiplied by a common ratio, resulting in discrete geometric growth.
Thus it is easy to present the geometric growth variables on a bar graph. The bar graphs will accurately represent the non-continuous geometric growth variables, making it easy to present and interpret data.
Therefore, it is possible to represent tangible items that cannot be less than one (i.e., people) using geometric growth bar graphs.
The sequence increase in the geometric growth is seen as growth, while a decrease is referred to as a decay sequence.
A geometric growth happens when a geometric function is multiplied by the same fixed number. If you multiply a function like f(x) by a variable ‘n’ new value, you will get a new discrete value.
The successive changes in the variable will be based on a constant ratio which is a distinct amount for the arithmetic change.
On the other hand, exponential growth happens when a function is raised to the same fixed power. You will get a new value each time you raise a function f(x) to some power, say ‘n.’
You can raise this new value to another power ‘n’ to achieve a newer value which gives a continuous change that might be represented on a graph.
What Is The Main Difference Between Exponential Functions And Geometric Functions?
Geometric growth happens when a function is multiplied by a fixed number. It is represented by a different function that gives discrete and non-continuous data.
For example, when a geometric function f(x) is multiplied by a number ‘n,’ it gives a new discrete value.
Geometric growth refers to a situation where the successive changes in a population differ based on a constant ratio which is a distinct amount for the arithmetic change.
However, exponential growth happens when a function is raised to the same fixed power every time.
You will get a new value when you raise a given function f(x) to some power, say ‘n.’ Then again, you can raise the new value obtained to power ‘n’ to get another newer value.
The result of the exponential growth is continuous data that a graph or curve can represent.
Therefore, geometric” implies rapid growth/decay but with a constant rate while “exponential” implies rapid growth/decay with an accelerating rate.
Why Is Exponential Growth Called Geometric?
Exponential growth is a generalization of geometric sequence which gives a continuous representation of data.
In a classroom, the teachers are more likely to use exponential growth to represent factors based on the mathematical factors presented.
Exponential growth is called geometric since it is not sustainable and depends on infinite resources. This model is applicable when there are few fixed variables and abundant resources.
Why Would You Use The Geometric Growth Model Instead Of The Exponential Growth Model?
Geometric growth happens when a function is multiplied by the same fixed number. You will get a new discrete value when you multiply a geometric function f(x) by a number ‘n.
Therefore, Geometric growth refers to the situation where successive changes in a variable differ by a constant ratio.
The geometric growth rates form annual growth rates, which dots can present on a graph or through bar graphs.
The geometric growth model gives the most accurate values. I could use it instead of the exponential growth model.
The geometric growth rate applies mostly to the compound growth over discrete periods, such as the payment and reinvestment of interest or dividends.
Thus, they give the correct mathematical representation of real-life issues, making it easy to solve mathematical problems.
Although continuous exponential growth might be more realistic, most economic phenomena are measured only at intervals.
Additionally, the exponential model promotes the idea of infinite resources, which can be shared among the existing variables.
We know that resources are scarce in most economic situations. In this case, the compound growth model is appropriate compared to the exponential growth model.
Similarities between Geometric Vs. Exponential Growth
Geometric and exponential growth concepts are used to represent and interpret data. When representing data, they consider factors such as increase, growth, multiplication, rebounds, depreciation, and decays. When solving a problem, it is better to read and understand the question and pay attention to the percentages, time length, and numbers when choosing geometric or exponential representation. You can calculate the common ratio when displaying a table of values for both the geometric and exponential growth values. The geometric distribution and exponential distribution belong to the exponential family
Math concepts such as geometric and exponential growth might be used interchangeably, but they have a few similarities and differences.
For instance, geometric growth refers to the situation where successive changes in a variable differ by a constant ratio.
On the other hand, exponential growth is a type of growth that happens when a function is raised to the same fixed power every time.
Both concepts apply to different mathematics situations, and you can choose one representing the given mathematical problem.