## Exponential Function in Excel

The exponential Excel function is also known as the EXP function in Excel, which is used to calculate the exponent raised to the power of any provided number. In this function, the exponent is constant and is also known as the base of the natural algorithm. It is an in-built function in Excel.

For example, if we want to determine the constant e to the power of provided numbers, we can use the Excel exponential (EXP) function in such a scenario. If the selected cell is D3, we will use the following formula:

**=EXP(D3)**

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### Exponential Function in Excel

Excel has an exponential Excel function called the EXP function, categorized as a Math/Trig function that returns a numeric value equal to **e **raised to the power of a given number.

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### Exponential Excel Formula

Exp function in Excel takes only one input, which is required; it is the exponent value raised to base **e.**

### What is e in Mathematics?

The number e is an irrational number whose value is constant and is approximately equal to 2.7182. It is also known as *Euler’s Number**.* The formula calculates the value of the number.

### How to Use EXP Function in Excel? (with Examples)

Like the LOG function is used when the rate of change in the data increases or decreases, the EXP function in Excel is used when data values rise or fall at increasingly higher rates.

In Excel, while working on non-linear trend lines (set of points on an exponential Excel function’s graph) or non-linear graphs, the EXP function in Excel is widely used.

An exponential function in Excel is also used to calculate the growth and decay of bacteria and microorganisms.

### Exponential in Excel Example #1

Suppose we have a sample for organic solutions. At time t=0 hours, the lab examiner puts one hundred bacteria into the solution to determine the suitable growth medium. After 5 hours, the examiner needs to calculate the count of bacteria. The growth rate of the bacteria in the given organic solution is 0.25/hour.

Total number of bacteria count at t=0 | 100 |

Total time for growth of bacteria (in hrs) | 5 |

Rate of Growth of Bacteria | 0.25 |

Total number of bacteria after 5 hrs | 129 |

For the rate of growth or decay, we have a formula:

*A=Pe*^{kt}

- Where A is the ending amount
- P is the initial amount
- t is the time of growth or decay
- k is the rate of decay or growth

In this case, A= 500, t = 5 hours, k = 0.25, P=?

So, to calculate the value of k in Excel, we have to use the exponential in Excel and the LOG function.

P = A/e^{kt}

Therefore, P = A/EXP(k*t)

In Excel, the formula will be:

**=ROUND(D3+D3/(EXP(G3*F3)),0)**

After 5 hours, the total number of bacteria in the given organic solution will be near around 129 in a count.

### Exponential in Excel Example #2

We have a function *f(x) *that is an exponential function in excel given as *y = ae ^{-2x}*where ‘a’ is a constant, and for the given value of x, we need to find the values of y and plot the 2D exponential functions graph.

x | 1 | 1.5 | 2 | 2.4 | 2.6 | 2.7 | 2.8 | 2.9 | 3 | 3.1 |

y | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? |

The value of a is 0.05

To compute the value of y, we will use the EXP function in Excel so that the exponential formula will be:

=**a* EXP(-2*x)**

Applying the exponential formula with the relative referenceRelative ReferenceIn Excel, relative references are a type of cell reference that changes when the same formula is copied to different cells or worksheets. Let's say we have =B1+C1 in cell A1, and we copy this formula to cell B2 and it becomes C2+D2.read more, we have

**=$B$5*EXP(-2*B2**

Applying the same exponential formula to other cells, we have:

Plotting the graph of the exponential function on the x-y axis, we have the following graph for the above-given function and values

### Exponential in Excel Example #3

Suppose we have the population data of 5 different cities given for 2001, and the rate of growth of the population in the given cities for 15 years was approximately 0.65%. Then, we need to calculate the latest population of the given cities after 15 years.

For the rate of growth, we have the formula:

**P = P _{0}*e^{rt}**

Where **P** is the latest population (which we will calculate in this case)

**P _{0}** is the initial population

**r** is the rate of growth

**t** is the time

Here, in this case, we have to calculate P for five different cities with the given rate of growth of 0.65

So, to calculate the rate of growth of the population, we will use the above population growth formula:

In Excel, to estimate the exponential power, we will further use the exponential function so that the exponential formula will be:

**=B2*EXP($F$1*$F$2)**

Applying the same exponential formula to other cities, we have:

**Output:**

The exponential function in Excel is also used to calculate the probability distribution in the statisticsStatisticsStatistics is the science behind identifying, collecting, organizing and summarizing, analyzing, interpreting, and finally, presenting such data, either qualitative or quantitative, which helps make better and effective decisions with relevance.read more. Hence, it is also known as the exponential probability distribution. The exponential distributionExponential DistributionExponential distribution refers to the continuous and constant probability distribution which is actually used to model the time period that a person needs to wait before the given event happens. This distribution is a continuous counterpart of a geometric distribution that is instead distinct.read more deals with the amount of time for a specific event.

The exponential function in Excel has also been used in the regressions linear modeling in the statistics.

**Things to Remember About Exponential Function (EXP) in Excel**

The exponential function in Excel is often used with the LOG function. So, for example, if we want to find the growth rate or decay, we will use the EXP and the LOG function together.

We can also use the POWER function in place of the exponential function in Excel. But, the only difference is the measurement precision. While using the POWER function, we can provide the of e as 2.71 or maybe up to 3-4 decimal places. However, in general, the EXP function in Excel takes the value of e to 9 decimal places.

So, suppose we are calculating an exponential in Excel series, dealing with a non-linear exponential functions graph with which we have the exponential value. Then, it is better to use the EXP function in Excel instead of the POWER functionPOWER FunctionPOWER function calculates the power of a given number or base. To use this function you can use the keyword =POWER( in a cell and provide two arguments one as number and another as power.read more.

The EXP function in Excel always takes the numeric value as an input. Therefore, if we provide any input other than the numeric value, it would generate the #NAME? Error.

While dealing with the complex exponents, for example, =EXP(-(2.2/9.58)^2), one should be careful with the brackets, if we mess up with the brackets, the output may differ from the actual output, so it should be =EXP(-((2,2/9,58)^2)).

### Recommended Articles

This article is a guide to Exponential Function in Excel. Here, we discuss the exponential formula and how to use EXP in Excel, exponential function examples, and downloadable Excel templates. You may also look at these useful functions in Excel: –