Knowledge of Exponential Growth Formulas

Exponential growth is an area of math that you get to notice in everyday life. Have you noticed how the streets seem to appear more crowded than before? That is because our population tends to grow exponentially. Exponential growth is a pattern of change in data that grows at a rate (the exponential factor) that increases over time. When plotted on a graph, it will show an increasing trend, rising sharply as it proceeds.

Understanding the concept:

Illustrating the concept with the help of an example, when things grow exponentially, they tend to increase faster every year. Let’s say that you start with a pair of pet mice, and their population achieves exponential growth. This means that in the first year, you will have:

YEAR	NO. OF MICE
1st	2
2nd	4
3rd	8
4th	16
5th	32
6th	64
7th	128

By the end of the 7th year, the population of mice, which continues to grow exponentially, will be well beyond your control! In the present case, we are talking about growth with the measly number of 2. But if you were to alter the number by just a little, the results change exaggeratingly.

YEAR	NO. OF MICE
1st	20
2nd	40
3rd	80
4th	160
5th	320
6th	640
7th	1280

Now imagine the same happening in the case of a population that lies in the hundreds of millions. Granted, many factors limit and slow down this growth, but even then, we are growing at a pretty exponential rate.

Tips to Avoid Confusion:

When you are a student of mathematics, you learn to get familiar with several formulas as each of them represents a different relation between numbers. Do not confuse exponential growth with linear growth or geometric growth. On the one hand, an exponential growth formula will increase in a multiplicative manner (5x5x5x5x… and so on). While on the other hand, a liner growth will grow in an additive manner (2+2+2+2+2+…. and so on), and a geometric growth will be showcased in a ‘raised to the power of’ manner (2525). Different kinds of growth formulas are used to denote different levels of growth. And all of them find an application in our daily life. However, in the present case, we will keep our focus only on understanding exponential growth formulas and how they play a vital role in our society. Formula: The formula for when things grow exponentially can be shown in the following manner: fx=a(1+r)x In the above-mentioned formula, f(x) = exponential growth function a = initial amount r = growth rate x = number of time intervals Now, if you want to find the value of any variable that tends to grow exponentially, all that you have to do is to put the values in the formula. Working out the final value of the equation is just a matter of simple calculations and can be done orally or with the help of a calculator.

Application:

The application of the concept is widespread. When you step out of the classroom into the real world, you see math happening all around you. From the change in population to the return that you get on your investment, everything is governed by the same formula. This is why exponential growth formulas have been around for such a long time. They have worked their way into the integrations and complexities of our daily life. Let us show you what it means with the help of an example. Suppose you decide to put USD1000 into your bank account. Now, if you are getting an interest rate of 10%, then your yearly return will be USD100 per year. This will keep on repeating as long as there is no change in the initial amount of your deposit, USD1000.But what if there was to be a change in it? What if you receive not simple interest but compound interest? Then your initial investment (provided that you do not make any other investments to change the growth rate) will grow at an exponential rate.The growth rate that you will achieve will be rapidly accelerating. It will outgrow the growth that it achieved last year. It will continue to grow in this manner unless there is any deduction in the amount accrued at the end of each fiscal cycle (in the case of the present example).

Conclusion

Although exponential growth formulas are pretty common and easy to understand, there are certain situations in which they do not hold practically. An example can be made of the stock exchange. You cannot predict the value that your stock or portfolio is going to hold in the long run because the principle values change over time. However, in situations that do not violate the fundamentals of exponential growth formulas, you get a correct answer by using the above-mentioned formula. We hope we have helped you grow exponentially in terms of knowledge.