Linear or exponential growth

Question

The population of a town is increasing by 620 people per year. State whether this growth is linear or exponential. If the population is 1400 today, what will the population be in three years?

Answer 1

If it is increasing at a constant rate of 620 per rear, the growth is linear.  The population obeys an equation of the form

 

P(t) = P₀ + at,

 

where

 

P₀ = population at time t = 0

a = linear growth rate of 620/year

t = years 

 

Let t = 0 be the year when P = 1400.  Then

 

P(t) = 1400 + 620t

 

P(3) = 1400 + 620(3) = 3260