The term “exponential growth” refers to anything which grows at an unbelievable or unreasonably quick rate. In some cases though, it has a more literal meaning. For instance, your personal or business income can experience exponential growth in a specific amount of time. You can use this exponential growth calculator to perform calculations whenever you need to. This makes the task easier, especially if you have to do several calculations.
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How to use the exponential growth calculator?
This exponential model calculator only requires some values for it to perform the calculations automatically. As long as you have these values, you will be able to acquire the results you need. Here are some steps to follow when using the exponential or population growth calculator:
- First, choose the Function from the drop-down menu. The choices include ex, 10x or ax.
- Then set the range of X from one value to another.
- Finally, input the value of the increment.
- After entering all of the required values, the exponential growth function calculator will automatically generate the values of X, Function, and a chart which shows the linear interpretation.
What is the formula for exponential growth?
Exponential growth may refer to different things. For instance, you’re a scientist who wants to study the growth rate of a new bacteria species. Although he can easily use an exponential growth calculator, he can also perform the computations manually.
To do this, he should first gather the data. If the scientist looks at his detailed records, he discovers that the starting population of the bacteria was 50. About 5 hours later, he discovered that the number grew to 500. To perform the calculation, the scientist can use this formula:
P(t) = P0ert
P(t) refers to the amount of some quantity at time t
P0 refers to the initial amount at time t = 0
r refers to the growth rate
t refers to the time or how many periods)
After the manual computation, he can check his work using the exponential growth and decay calculator. If he performed the calculation correctly, then it’s time to interpret the results.
What is exponential growth rate?
As aforementioned, the exponential growth rate may refer to several things. This means that it can also mean a specific variable’s change in percentage within a specific period of time and in a specific context. For an investor, an exponential growth rate would be ideal. This is especially true if it refers to the growth rate of the earnings, dividends, revenues, retail sales, and other macro concepts of the company.
The exponential growth rate can also represent a pattern of information which shows higher increases as time passes by thus, creating an exponential function curve. When plotted on a chart, the curve would begin slowly, stay flat for some time, then increase exponentially until it becomes almost vertical.
In the world of finance, compound returns are the ones which cause exponential growth. This is because compounding is very powerful, especially in this industry. The concept permits investors to come up with huge sums using minimal initial capital. A common example of this concept is a savings account which carries a compounding interest rate.
How do we calculate growth rate?
When you hear the words “calculate growth rate,” you might get intimidated. In such a case, you may want to use an exponential growth calculator if you feel that manually calculations would be too much of a challenge. But the truth is, performing the calculation is quite simple. Here are some steps:
Calculate the basic growth rate
- Acquire the data you need which shows a change in the quantity over a specific amount of time. When calculating the basic growth rate, you only need two values namely the starting quantity value and the ending quantity value. To illustrate this better, let’s use actual values for example. Let’s set the starting quantity value at 205 and the ending quantity value at 310.
- Now you can use the formula for growth rate:
Growth rate = ending value – starting value / starting value
- The value you will acquire will be in fraction form. To convert this into a decimal value, divide the fraction:
Growth rate = (310 – 205) / 205 = 105 / 205 = 0.51
- The next thing to do is convert the decimal value into a percentage value. Do this by multiplying the answer you obtained by 100 then add the percentage sign:
Percentage conversion = 0.51 * 100 = 51%
Calculate the average growth rate over regular intervals of time
- You must organize all of your data in a table. Although this isn’t a necessary step, it can be very useful later on. It will help you visualize the data as a range of values over a specific period of time. Create a table with two columns. List the time values on the left side and the corresponding quantity values on the right.
- The data you input must possess regular values for the time intervals, and they must have a corresponding quantity value. Use the past values and the present values with a new formula:
(present) = (past) * (1 + growth rate) n
where n refers to how many time periods
- Performing this calculation will provide you with an average growth rate for every time interval for the past and the present figures. Of course, we’re assuming that there’s a steady growth rate.
- Isolate the value of the “growth rate.” Make a modification to the formula to obtain this variable:
Growth rate = (present / past) 1 / n – 1
- Use the formula to calculate the growth rate by inserting all the values needed. Then solve for the final growth rate using the basic algebraic principles. Going back to our example, let’s say that the time period n is 9 years. Using the formula:
Growth rate = (310 / 205) 1 / 9 – 1 = .0422
Percentage = .0422 * 100 = 4.22%