Question

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

Modeling
ANSWERED
asked 2021-02-05
A population of 6 mice doubles every 4 weeks. When will this population reach 120 mice? Use an algebraic solving process.

Answers (1)

2021-02-06

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 \(\begin{array}{|c|c|}Population\ of\ mice (y) & 6 & 12 & 24 48 & 96 & 192 \\ \hline no. of weeks(x) & 0 & 4 & 8 & 12 16 & 20\end{array}\) Using this data, modeling the equation between the Population of mice (y) and no. of weeks(x) So, the modeled equation is \(y = 6*2^{x/4}\) Now we want \(y= 120, then\ x=?\) Substituting \(y = 120\ in\ the\ y = 6*2^{x/4}\) \(120 = 6^*2^{x/4}\)
\(2^{x/4} = 120/6\)
\(2^{x/4} = 20\) Taking logarithm both sides \(\ln2^{x/4} = \ln20\)
\(x/4*\ln2 = \ln20\) \((\because \ln MP = p\ln M)\)
\(x = \frac{4\in 20}{\ln2}\)
\(x=17.3\) So, it takes 17.3 weeks to reach the population of mice 120

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