Question

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?

Answer 1

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

Answer 2

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.))`)