(a) The simple logistic growth model given as equation 17.3 in the text GS g S S ( ) = − S 

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 1  MAX gives the amount of biological growth, G, as a function of the resource stock size, S. This equation can be easily solved for S = S(t), that is, the resource stock as a function of time, t.
The solution may be written in the form S t S k gt ( ) = + −
MAX where k = (SMAX − S0)/S0 and S0 is the initial stock size (see Clark, 1990, p. 11 for details of the solution). Sketch the relationship between S(t) and t for:
(i) S0 > SMAX (ii) S0 < SMAX *

(b) An alternative form of biological growth function is the Gompertz function Use a spreadsheet program to compare – for given parameters g and SMAX – the growth behaviour of a population under the logistic and Gompertz growth models.