Short 3 part question

Question

The population P of a city has been increasing at an annual rate of 2.3%. It's population was 150 million in 2008 and P is in millions.
a. Use the pert general formula to create a specific formula P(t) for finding the population when t is the number of years after 2008 and P is millions
b. estimate the population in 2018
c. In what year will be the population be double what it was in 2008

Answer 1

Tevan,

The general pert equation is P_t = P₀(1+r)^t, where P₀ is the initial population, r is the growth rate in decimal form, and P_t is the population after t years of growth.

 

a)   P(t) = 150(1.023)^t

 

b)   t = 2018 - 2008 = 10, so

      P(10) = 150(1.023)¹⁰ = 188.3 million

 

Double the population of 2008 is 2 * 150 = 300 million

 

c)    300 = 150(1.023)^t

 

          2 = (1.023)^t

 

        ln(2) = t(ln(1.023))

 

          t = ln(2)/ln(1.023) = 30.5

 

          2008 + 30.5 puts you in the year 2038