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bbolker / math3mb

Mathematical Modelling at McMaster University
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Tim Hortons Model #3

Closed wang988 closed 6 years ago

wang988 commented 6 years ago

I have a question about the Tim Hortons Model. N(0)= 87, the rate is +3 per year. Why is it a decreasing function?

bbolker commented 6 years ago

The rate of addition of new stores is 3 per year. However, only 90% of existing stores/survive 10% of existing stores are lost every year (the formula is N(t+1)=3+0.9*N(t)). If we start with more than the equilibrium level (a/(1-b) = 3/(1-0.9) = 30), then more old stores are being lost each year than new ones added. For example, suppose we start with 90 stores. 10%, or 9, are lost, 3 are added, for a net loss of 6.

Does that make sense?

wang988 commented 6 years ago

Oh thanks I see! I remember the assumption was lifetime=10 years. Now I understand Thank you!