The population of a town grows at a rate proportional to the

The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 5% in 10 years.

a)What will be the population in 30 years? Round to the nearest person.

b) How fast is the population growing at t = 30?

Solution

We use the exponential growth model with n0 = 500 and rate of growth = 50 % = 0.05 in 10 years

Hence, for 30 years we use 3

a) f(t) = 500 e^0.05t

   f(30) = 500*e^0.05*3

   = 580.9171

(b) original population = 500, New population = 581 (aprrox)

change in population 581 -500 = 81

Population Growth at t=30, = 81/500 = 16.18%