How to Plot Logistic Growth in Excel
By Chris Daniels
Logistic growth begins as exponential growth that eases to a steady equilibrium value. Seen in population growth, logistic function is defined by two rates: birth and death rate in the case of population. The logistic growth function is bounded by two equilibria: the case of zero population or equal birth and death rates. Logistic growth in business may be applied to modeling the size of companies or the extent of a market. However logistic growth modeling applies to your business, Microsoft Excel provides professional charting and modeling tools to professionally present your results.
Create Logistic Plot
Launch Microsoft Excel and load a worksheet with existing data or create a new worksheet.
Click on the "Insert" tab and select a chart style beneath the Charts heading. Choose a line, area or scatter plot to best display logistic growth data.
Input the cell range for the x and y data values for your logistic growth curve. Typically, x corresponds to time and y correspond to a measure such as population, market capitalization or number of employees. If you have data selected when you click on the chart option, it will be automatically entered into the data range text box.
Simulate Logistic Data
Use an existing time base or create a new one. This is the range of time that you will calculate logistic growth data for. Select a new data column, label it accordingly and enter the first two values. This may be 1 and 2 or 1,000 and 1,001. With both cells selected, drag the black fill handle box outlining the selection until as many cells as you wish are filled. Excel will detect the pattern set by the first two cells and use it to generate the rest of the data.
Select a new cell and label it "Stable Value." Enter the value you wish to correspond to the stable value of the logistic growth. In the case of population growth, this will be the point where the birth and death rate are equal.
Select another new cell and label it "Rate." Enter the value corresponding to the initial rate of exponential growth in the population.
Select another new cell and label it "Initial Value." Enter the initial value to start simulating the logistic growth from. To be meaningful, this must be a value greater than zero.
Select a new data column and label it "Logistic Growth Value." Enter the following formula in the Excel formula box to calculate logistic growth values using the other parameters.
\= K / (1 + ((K - Y0) / Y0) * EXP(R * T))
Replace K with the "Stable Value" cell, Y0 with the "Initial Value" cell, R with the "Rate" cell and T with the corresponding "Time" cell. If these were in columns A, B, C and D, respectively, the formula would read:
\= A1 / (1 + ((A1 - B1) / B1) * EXP(C1 * D$1))
Chris Daniels covers advances in nutrition and fitness online. Daniels has numerous certifications and degrees covering human health, nutritional requirements and sports performance. An avid cyclist, weightlifter and swimmer, Daniels has experienced the journey of fitness in the role of both an athlete and coach.