What is a formula to show this? In which year will the population exceed 10000 people?

Question

in 2014 the population was 220. The population increases at a rate of 35% each year. What is a formula to show this? In which year will the population exceed 10000 people

Answer 1

The formula for Future Value is FV = Current value times (1 rate/year)^{number of years}

 

in this case, FV = 10,000; Current value = 220; rate = 35% or 0.35, and we want to solve for the number of years

 

our formula becomes 10,000 = 220 * (1.354)ⁿ

which becomes 10,000/220 = (1.354)ⁿ

 

you can solve this equation using logarithms, and the answer will be ≅ 12.7 years

 

or, you can use Excel, and create a table of values, and the answer will be the same