Exponential growth occurs when the factor by which a quantity increases is const

Question

Exponential growth occurs when the factor by which a quantity increases is constant - i.e., it is multiplies by the same quantity at each time step. What if, instead, the same amount was added to the quantity at each time step? Consider the case in which a population of rabbits increases by 10 rabbits each generation.

(a) what is the function that corresponds to this type of growth?

(b) What is the long-term behavior of the orbit?

(c) Let P0 be the intitial number of rabbits. Find a function P(t) that gives the number of rabbits as a function of time.

Explanation / Answer

(a) P(t+1) = P(t) + 10

This is a linear function

(b) In Long term , the population keeps on increasing with a constant rate of 10.

(c) P(t) = P(t-1) + 10 = P(t-2) + 2 x 10 = P(t-3) + 3 x 10 = P(t - t ) + 10 t = P(0) + 10 t

Therfore P(t) = P0 + 10 t  

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