A town has a population of 13000 and grows at 2.5% every year. What will be the population after 5 years, to the nearest whole number?

Answer 1

Suppose you had to determine the population after one year.

13000 + (0.025)13000

13000(1 + 0.025) Notice how the 13000 was factored from both terms.

13000(1.025) ; increasing 13000 by 2.5% is the same as multiplying 13000 by 1.025

13325 is the population after one year.

For year two you can follow the same pattern:

13325(1.025)

13658.125

And so on. This is an exponential growth function, which can be written like this:

P(t) = 13000(1.025)^t

Note:

P(0) = 13000 (the initial value of the population)

P(1) = 13000(1.025)¹

P(2) = 13000(1.025)(1.025) which gives the 13658.125

P(3) = 13000(1.025)³ = 13999.578

P(5) = 13000(1.025)⁵ = 14708.307 (rounded to nearest whole number: 14708)

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