The Excel EXP function is also known as an exponential function. It is mainly a mathematics formula that returns the value of the constant e raised to the power of a given number. Whenever data values increase or fall exponentially (at an increasingly higher rate) then the EXP function helps to calculate the rate of growth or decay.
In this article, I will show you various examples of how you can use the Excel EXP function.
EXP Function in Excel: Syntax
The EXP function calculates and returns the value of the constant e raised to the power of a given number. Here, e is a numeric constant, and the value of constant e is approximately ≈ 2.71828.
The constant e denotes exponential growth and decay. The formula is ex.
|The power that e is raised to
The EXP function returns the constant e raised to the power of a number.
The EXP function is available for Excel 2000 and later versions.
1. Using The EXP Function to Get e Raised to The Power of a Number
To find the value of the constant e raised to a given number, you can use the EXP function.
Here, The EXP function mathematically form is ex or e^(number).
Now, I’m going to pass the number -1 as the argument in the EXP function.
⏩ In cell D4, type the following formula to get the exponential value of the number -1.
Here, in the EXP function, I selected the B4 cell as a number.
Then, press ENTER, and the EXP function will return an exponential value of the selected cell B4. Here, e raised to power -1.
You can follow the same process, or you can use the Fill Handle to get e raised value of the power of other values.
Here, you will get the value of e against the value 1 which is 2.718281828. It is known as the constant of e.
2. Using Excel EXP Function to Get The Rate of Growth Or Decay
You can use the EXP function along with the ROUND function to calculate the growth and decay of bacteria, viruses, and microorganisms.
Let me describe the process with an example. To demonstrate the procedure, I’m going to use a dataset that contains a virus count.
I’ve taken a sample of organic solutions. The information on the solution is given below.
Here, I want to calculate the count of viruses after 7 hours.
As we know, we have the formula to calculate the rate of growth or decay is
The formula expressions meaning is,
A = The ending amount that we want to calculate
P = It is the initial amount provided in the solution, 250
t = It is the time of growth or decay, 7 hours
k = It is the rate of decay or growth, 0.38
To calculate the ending amount of virus (A) after 7 hours. I going to use the described formula by using the EXP function. Which will be A = P* EXP(k*t).
Here, In the ROUND function, I used (D6*(EXP(D7*D8) as number and 0 as num_digits.
In the EXP function, selected both the cells D7 and D8 as numbers then multiplied it to get e raised value of the given number of both cells.
Then multiplied the exponential value with the D6 cell and passed the result to the ROUND function to get only the integer value.
Now, press ENTER, and you will get the total number of viruses after 7 hours in the solution.
3. Calculating Rapid Growth with The EXP Function in Excel
Several times the earth faced virus or bacteria-infected diseases with a huge number of infections. In 2019 coronavirus came with a few numbers of infected cases but within 2020 it spread all over the planet. To track the spread of such types of virus or bacterial infections we can use the EXP function.
Here, I’m going to use a sample dataset to show you how we can use the EXP function to calculate the rate of growth of such types of data values.
To calculate how many persons have been infected at any time, I’m going to use the mathematical equation,
N = N₀eᵃᵗ
The equation expressions meaning,
N = Total number of people infected by virus
a = Rate of infection
t = Time (you can use day, hours, years, etc)
N0 = Initial number of infected people
⏩ In cell D9, type the following formula to get the growth of the virus.
Here, In the EXP function, selected both the cells C7 and C8 as numbers then multiplied it to get e raised value of the given number of both cells.
Then multiplied the exponential value with the C6 cell to get the number of infected people after 30 days.
Now, press the ENTER key and you will get the total number of infected people after 30 days of the spread of the virus.
If you want, you can use the ROUND function to get the round figure or only the integer number explained in Example 2.
4. Using EXP Function to Calculate Unknown Variable
To plot any 2D graphs first you will need the values of the corresponding function. In case you have any exponential function then you can use the EXP function to calculate the function with exponent.
Here, I’m going to describe an exponential equation that is y = ae.-2x. I’m going to use a dataset where I have the values of x and the slope which is denoted as a which is constant.
The formula is going to look like with the EXP function is,
y =a* EXP(-2*x)
⏩ In cell C7, type the following formula.
Here, In the EXP function, selected the cells C6 and multiplied it with -2 to get e raised value of the given number.
Then, multiplied the exponential value with the $E$4 cell which has the constant value of a. Here, I used absolute reference for the E4 as it is a constant value.
Now, press the ENTER key and you will get the value of Y.
Now, by using the Fill Handle, you will get all the values of y for corresponding x.
Read More: How to Calculate Exponential in Excel
5. Calculating Population Growth with EXP Function in Excel
To calculate the latest population of any city or country you can use the EXP function.
Here, I’ve taken a dataset of a couple of countries to calculate the population rate for 10 years. Also, I took the approximate rate of growth for all countries.
To calculate the population growth, I’m going to use an equation that is
P = P₀*e
The formula expressions are,
P = Latest population
r = Rate of population growth
t = Time (years)
P0 = Initial population
⏩ In cell E4, type the following formula to get the growth of the virus.
Here, In the EXP function, selected the absolute reference of cells $D$4 and $D$5 because the value of D4 and D5 are constant for other countries also. Then, multiplied both values to get e raised value of the given number.
Again, multiplied the exponential value with the C8 cell to get the population of 2020.
Now, press the ENTER key and you will get the population for 10 years.
As the rate of growth and time is the same for other countries so you can use the Fill Handle to get the population of 2020.
Read More: How to Make Exponent in Excel Text
Things to Remember
🔺 The EXP Function only takes the numeric values as an input. It shows the #VALUE error for non-numeric values.
🔺 Always be careful while using complex exponents formulas, if you misplace any brackets, you will get incorrect output.
Download to Practice
In this article, I have shown 5 examples of the Excel EXP function. I also tried to cover the when and why the EXP function may show errors frequently. Last but not least, if you have any kind of suggestions, ideas, or feedback please feel free to comment down below.