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natulia [17]
3 years ago
15

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 doub

le at this growth rate? Explain
Mathematics
1 answer:
charle [14.2K]3 years ago
3 0
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
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