A town has a population of 5000 and grows at 2% every year. What will be the population after 5 years, to the nearest whole number?

Question

A town has a population of 5000 and grows at 2% every year. What will be the population after 5 years, to the nearest whole number?

Answer 1

P(t) = population t years after it started at P₀

P(t) = P₀(1.02)^t

P₀ = initial population

t = years elapsed since it started at P₀

P(t) = 5000 (1.02)^t

P(5) = 5000(1.02)⁵ = 5520 (rounded to the nearest whole number)

Answer 2

Hello Tyla!

This questions has a similar concept to compound interest. Let me explain:

After one year, the population will be:

5000 + 5000*2% = 5000*(1+2%) = 5000*(1.02)

After two years, the population will be:

5000*(1.02)*(1.02) = 5000*(1.02)²

Then, after 5 years, the population will be:

5000*(1.02)⁵ = 5,520

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