Numerically Approximating rate of change worksheet
A worksheet for derivative calculation:
Lab 3 Part I, Calculus I
Unity College, Carrie Diaz Eaton
Consider an environmental indicator which can be described by the following equation:
where t is in years.
Sketch a graph of P(t) and from that, sketch what you expect P’(t) to look like.
Write an equation for P(t+∆t)
Try to calculate the derivative algebraically using the limit definition of derivative
Create a spreadsheet that calculates the derivative numerically at 21 different points of the graph: t = 0, .5, 1, 1.5, … 10
(Hint: Create a table for with 21 rows (t = 0, .5, 1, 1.5, … 10) and 8 columns: t,P(t), then for∆t=1 P(t+∆t), P/∆t=[P(t+∆t)-P(t)]/∆t, then for∆t=.1 P(t+∆t), P/∆t=[P(t+∆t)-P(t)]/∆t, and for∆t=.01 P(t+∆t), P/∆t=[P(t+∆t)-P(t)]/∆t.)
Results Graph a scatterplot of P(t) and your estimates of P’(t) based on the numerical work performed in #4.
Discussion Do the visual results based on visual, algebraic and/or numerical work agree?
Discussion Contrast the initial and long-term value of the instantaneous rate of change.
Discussion Suppose a different function was hypothesized for P(t), such as t^2 or e^(-t). How would you modify your spreadsheet to approximate the graph of the derivative?
Timothy John Beaulieu onto Derivatives