A Logistic Model of Sunflower Growth This problem involves planting a sunflower seed...

A Logistic Model of Sunflower Growth This problem involves planting a sunflower seed and plotting the height of the sunflower versus time. It should take 3–4 months to gather the data, so start early! You can substitute a different plant if you like, but you may then have to adjust the time scale and the height scale appropriately.

(a) You are going to be creating a plot of the sunflower height (in cm) versus the time (in days). Before beginning, guess what this curve is going to look like, 1 hour 2 and fill in your guess on the grid.

(b) Now plant your sunflower. Take a height measurement the first day that your flower sprouts, and call that day 0. Then take a measurement at least once a week until it is time to start writing up your data.

(c) Do your data points more closely resemble exponential growth or logistic growth? Why?

(d) If your data more closely resemble exponential growth, the equation for height versus time will be If your data more closely resemble logistic growth, the equation for height versus time will be What is the physical meaning of C? Use your data to estimate C.

(e) We now experimentally determine k. At each of your t values, estimate by using difference quotients. Then use the fact that to get a best estimate of k.

(f) Solve your differential equation. Now graph your solution along with the data points. Did you come up with a good model? Do you think that k will change if you plant a different sunflower next year?