### Using Calculus to Model the Growth of the Tree Liquidambar Styrsciflua (American Sweetqum)

## by Laura Borgerding

Submitted : Spring 2016

The researcher uses a simple method to find the area of a leaf without damaging the leaf, allowing for multiple readings of the area and to be able to track the growth of the leaf. With the data found, using time, *t*, and area, A, the researcher finds the constants of the Gompertz equation that best fit the data points. Using the Gompertz equation, the researcher was able to project a more complete curve of the total growth of the leaf, found in Figure 2. Next, the derivative of the initial Gompertz equation was taken to find the equation of the growth rate. The rate of growth is variable, and is therefore not exponential or linear. Using the derived equation, the curve for the growth rate was projected, showing the maximum growth rate around day 9 of growth (See Figure 3). Many variable affect the growth of a plant, such as access to the sun, preferred soil, and water supply. Other researchers can compare their rate of growth of the same species of tree to these projections, and determine, which climate and environment the plant is more suited for.

[ Back ]