Fitting Exponential and Logistic Growth Models to Bacterial Cell Count Data

In this activity, students will model a noisy set of bacterial cell count data using both exponential and logistic growth models. For each model the students will plot the data (or a linear transformation of the data) and apply the method of least squares to fit the model's parameters. Activities include both theoretical and conceptual work, exploring the properties of the differential equation models, as well as hands-on computational work, using spreadsheets to quickly process large amounts of data. This activity is meant as a capstone to the differential calculus portion of a typical undergraduate Calculus I course. It explores a biological application of a variety of differential calculus concepts, including: differential equations, numerical differentiation, optimization, and limits. Additional topics explored include semi-log plots and linear regression.

在本活动中，学生将利用指数和逻辑增长模型对一组噪声细菌细胞计数数据进行建模。对于每个模型，学生将绘制数据图（或数据的线性变换图），并应用最小二乘法来拟合模型参数。活动包括理论与概念性工作，探索微分方程模型的特点，以及实际计算工作，利用电子表格快速处理大量数据。此活动旨在作为典型本科生微积分I课程微分部分的一个总结。它探讨了多种微分计算概念在生物学中的应用，包括：微分方程、数值微分、优化和极限。此外，还探讨了半对数图和线性回归等额外主题。