# A population of 6 mice doubles every 4 weeks. When will this population reach 120 mice? Use an algebraic solving process.

usagirl007A 2021-02-05 Answered
A population of 6 mice doubles every 4 weeks. When will this population reach 120 mice? Use an algebraic solving process.
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## Expert Answer

Yusuf Keller
Answered 2021-02-06 Author has 90 answers

Step 1 Given, A population of 6 mice doubles every 4 weeks. We have to find when population reach 120 mice Step 2 Now making the table of data Using this data, modeling the equation between the Population of mice (y) and no. of weeks(x) So, the modeled equation is $y=6\ast {2}^{x/4}$ Now we want Substituting $120={6}^{\ast }{2}^{x/4}$
${2}^{x/4}=120/6$
${2}^{x/4}=20$ Taking logarithm both sides $\mathrm{ln}{2}^{x/4}=\mathrm{ln}20$
$x/4\ast \mathrm{ln}2=\mathrm{ln}20$ $\left(\because \mathrm{ln}MP=p\mathrm{ln}M\right)$
$x=\frac{4\in 20}{\mathrm{ln}2}$
$x=17.3$ So, it takes 17.3 weeks to reach the population of mice 120

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Jeffrey Jordon
Answered 2021-10-27 Author has 2262 answers

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