The population of Springfield is currently 41,250. If Springfield’s population increases by 2% of the previous year’s population, use this information to find the population after 4 years?

2 Answers
Jul 3, 2018

population after 4 years is 44,650 people

Explanation:

Given: Springfield, population 41,250 is increasing population by 2 % per year. What is the population after 4 years?

Use the formula for increasing population: P(t) = P_o (1 + r)^t

where P_o is the initial or current population,

r = rate = %/100 and t is in years.

P(4) = 41,250 (1 + 0.02)^4 ~~ 44,650 people

Jul 3, 2018

Years in order: starting with a population of 41,250 people

  1. 42,075 people
  2. 42,917 people
  3. 43,775 people
  4. 44,651 people

Explanation:

t_(0)=41,250 (the zero means your starting point)

Your rule for population increase in Springfield is
t_a=t_(a-1)+0.02(t_(a-1))

a means population you are about to calculate and a-1 means the next year's population.

Therefore...

  • a=0 with 41,250 people
  • a=1 with 42,075 people
    41,250+0.02(41,250)=41,250+825=42,075
  • a=2 with 42,917 people
    42,075+0.02(42,075)=42,075+841.5=42,916.5\approx42,917
    (\color(indianred)(\text(You cannot have half a person, so round up.)))
  • a=3 with 43,775 people
    42,917+0.02(42,917)=42,917+858.34=43,775.34\approx43,775
    (\color(indianred)(\text(You cannot have half a person, so round down.)))
  • a=4 with 44,651 people
    43,775+0.02(43,775)=43,775+875.5=44,650.5\approx44,651
    (\color(indianred)(\text(You cannot have half a person, so round up.)))