lisapressley2001 lisapressley2001

05-01-2017
Mathematics

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Suppose the population in a town average growth rate of 18% if there are 15500 people now living in town in about how many years will the population grow to 30,000? Use the equation 30,000=(15,500)(1.18)^x and around the value of x to the nearest year

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LammettHash LammettHash

05-01-2017

This is just a matter of solving for [tex]x[/tex] in the given equation.

[tex]30000=15500\times1.18^x[/tex]
[tex]\implies 1.935=1.18^x[/tex]
[tex]\implies \log_{1.18}(1.935)=\log_{1.18}(1.18^x)[/tex]
[tex]\implies 3.988=x\implies x\approx 4\text{ years}[/tex]

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