Nine unidentified plants have been discovered on an isolated island on the West Coast. While unknown, their properties have been carefully catalogued by a team of chivalrous botanists in order to link them to other similar species located in nearby ecosystems.

The size S (in cm) of these plants is given by the following equation:

S(t)=Smax1+e−r(t−50)

Growth rates r (cm/months) for each plant= 0.07, 0.12, 0.16, 0.18, 0.15, 0.2, 0.6, 1.0, 0.25

Maximal observed sizes Smax (cm) for each plant = 40, 45, 80, 34, 24, 78, 89, 45,140

a) (0.5 point) Create lists/arrays with the values of the growth rates and maximal observed sizes. Print them.

b) (0.5 point) Define a function called Size(r, S_max, t) that takes the growth rate r, maximal size S_max and time t (in months) as inputs and returns the size of a given plant on this island.

c) (1 points) Use this function and your arrays/lists to plot the size as a function of time, for a period of 100 months with steps of 1 month, of all the plants studied, on the same plot. Include axe labels and title. By looking at the plots, what type of growth does it correspond to?

d) (1 point) Create the 3x3 subplot where all growth curves are now plotted in different panels. (HINT: The function plt.tight_layout() will help out cleaning the resulting plot. Use it at the end of your code. )

e) (1 points) The plants are all fighting for limited ressources and also sunlight. Indexing the plants from 1 to 9 (according to the order in which they appear in your arrays defined in a), find and plot the index of the largest plant as a function of time. Describe your results. (HINT: the function np.argmax(A) returns the index of the maximal entry of an array A)