If bacteria are cultured in a medium with limited nutrients, competition ensues and growth slows. According to Verhulst's model, the number of bacteria at 40-minute intervals is given by

where K is a constant. 

(a) Let a = 200 and K = 10,000. Graph the sequence for n = 1, 2, 3,.... 20. 

(b) Describe the growth of these bacteria. 

(c) Trace the graph of the sequence. Make a conjecture as to why K is called the saturation constant. Test your conjecture by changing the value of K.

Transcribed Image Text:

an = 2 1+ a-1/K n-1-