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The population of a town has grown at an annual rate of 2.7%. How long does it take for it’s population of 18,450 people to double at this growth rate? Explain

User Brushleaf
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It would take 26 years.

The equation will be in the form y = a(1+r)ˣ, where a is the initial population, r is the growth rate as a decimal number, and x is the amount of time. Using our information we have

y = 18450(1+0.027)ˣ = 18450(1.027)ˣ

We want the population to be doubled; 18450*2 = 36900:
36900 = 18450(1.027)ˣ

Divide both sides by 18450:
36900/18450 = 18450(1.027)ˣ/18450
2 = 1.027ˣ

Using logarithms, we have

\log_(1.027)2=x \\ \\x=26.017
User Zerey
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