Overview
A trendline is a line superimposed on a chartrevealing the overall direction of the data. Google Charts canautomatically generate trendlines for Scatter Charts, Bar Charts,Column Charts, and Line Charts.
Google Charts supports three types of trendlines: linear,polynomial, and exponential.
Jun 01, 2017 Re: Exponential Trendline formula Since you have an exponential trendline, I'll assume you know what an exponential trendline is. The equation for an exponential curve is y = a e b x, where a and b are arbitrary constants and e is the mathematical constant e.
Linear trendlines
A linear trendline is the straight line thatmost closely approximates the data in the chart. (To be precise, it'sthe line that minimizes the sum of squared distances from every pointto it.)
In the chart below, you can see a linear trendline on a scatterchart comparing the age of sugar maples to the diameter of theirtrunks. You can hover over the trendline to see the equationcalculated by Google Charts: 4.885 times the diameter + 0.730.
To draw a trendline on a chart, use the
trendlines
option and specify which data series to use:Linear trendlines are the most common type of trendline. Butsometimes a curve is best for describing data, and for that, we'llneed another type of trendline.
Exponential trendlines
If your data is best explained by an exponential of theform eax+b, you can use the exponential trendline, asshown below:
type
attribute to specify an Note: Unlike linear trendlines, there are several differentways to compute exponential trendlines. We provide only one methodright now, but will support more in the future, and so it's possiblethat the name or behavior of the current exponential trendline willchange.
For this chart, we also use
visibleInLegend: true
todisplay the exponential curve in the legend.Changing the color
By default, trendlines are colored the same as the data series, butlighter. You can override that with the
color
attribute.Here, we chart how many digits of π have been calculated by yearduring a computationally fruitful period, coloring the exponentialtrendline green.Here's the trendlines spec:
Polynomial trendlines
To generate a polynomial trendline, specifytype
polynomial
and a degree
. Use withcaution, since they can sometimes lead to misleading results. Inthe example below, where a roughly linear dataset is plotted with acubic (degree 3) trendline:Note that the plummet after the last data point is only visible because we artificially extended the horizontal axis to 15. Without setting hAxis.maxValue to 15, it would have looked like this:
Same data, same polynomial, different window on the data.
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Exponential in Excel (Table of Contents)
Exponential Function in Excel
Excel has an exponential excel function called EXP function which is categorized as Math/Trig Function that returns a numeric value which is equal to e raised to the power of a given number.
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. This is number is also known as Euler’s Number. The value of the number is calculated by the formula
How to Use EXP Function in Excel? (with Examples)
Like LOG function is used when the rate of change in the data increases or decreases quickly, the EXP function in Excel is used when data values rise or fall at increasingly higher rates.
In Excel, while working non-linear trend lines (set of points on an exponential excel function’s graph) or non-linear graphs EXP function in Excel is widely used.
An Exponential function in Excel is also used to calculate the growth and decay of a bacteria and microorganisms.
You can download this Exponential Function Excel Template here – Exponential Function Excel Template
Exponential in Excel Example #1
Suppose we have a sample for organic solutions, the lab examiner at time t=0 hours puts one hundred bacteria into the solution in order 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
For the rate of growth or decay, we have a formula
A=Pekt
![Exponential Exponential](/uploads/1/2/5/8/125805072/685808838.png)
- 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 in order to calculate the value of k in Excel, we have to use the exponential in excel and log function
P = A/ekt
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-2xwhere ‘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.
The value of a is 0.05
To compute the value of y we will use the EXP function in excel so the exponential formula will be
=a* EXP(-2*x)
Applying the exponential formula with the relative reference we have
=$B$5*EXP(-2*B2
Applying the same exponential formula to other cells, we have
Plotting the exponential functions graph on the x-y axis we have the following graph for the above-given function and values
Exponential in Excel Example #3
Suppose we have the population data of 5 different cities given for the year 2001, and the rate of growth of the population in the given cities for 15 years was approximately 0.65%. We need to calculate the latest population of the given cities after 15 years.
For the rate of growth, we have the formula,
P = P0*ert
Where P is the latest population (which we will calculate in this case)
P0 is the initial population
r is the rate of growth
t is the time
Here, in this case, we have to calculate P for five different cities with the given rate of growth of 0.65
So in order to calculate the rate of growth of the population we will use the above population growth formula
In Excel to calculate the Exponential power we will further use the Exponential Function in Excel, so the exponential formula will be
=B2*EXP($F$1*$F$2)
Applying the same exponential formula in reference to other cities we have
Output:
The Exponential Function in Excel is also used for also calculating the probability distribution in the statistics also known as the exponential probability distribution. The exponential distribution deals with the amount of time for a specific event to occur.
The Exponential function in Excel is also 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, for example, in case, if we want to find the rate of growth or decay, in that case, 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 may be up to 3-4 decimal places, however, the EXP function in excel, in general, takes the value of e to 9 decimal places.
So, if are calculating an Exponential in excel Series, of dealing with non-linear exponential functions graph in which we have the Exponential value, it is better to use the EXP function in excel instead of the POWER function.
EXP function in excel always takes the numeric value as an input, if we provide any other input other than the numeric value it generates #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 has been a guide to Exponential Function in Excel. Here we discuss the Exponential Formula and how to use EXP in Excel along with Exponential Function examples and downloadable excel templates. You may also look at these useful functions in excel –
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