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The table below shows the population of a group of mice over a period of time.
POPULATION OF MICE





Month
0
1
2
3
4


Population
4
8
16
32
64




If this pattern continues, what will be the population of mice in Month 12?
A. 192
B. 4,096
C. 8,192
D. 16,384

33. The table below shows the population of a group of mice over a period of time.\newlinePOPULATION OF MICE\newline\begin{tabular}{|l|c|c|c|c|c|}\newline\hline Month & 00 & 11 & 22 & 33 & 44 \\\newline\hline Population & 44 & 88 & 1616 & 3232 & 6464 \\\newline\hline\newline\end{tabular}\newlineIf this pattern continues, what will be the population of mice in Month 1212?\newlineA. 192192\newlineB. 44,096096\newlineC. 88,192192\newlineD. 1616,384384

Full solution

Q. 33. The table below shows the population of a group of mice over a period of time.\newlinePOPULATION OF MICE\newline\begin{tabular}{|l|c|c|c|c|c|}\newline\hline Month & 00 & 11 & 22 & 33 & 44 \\\newline\hline Population & 44 & 88 & 1616 & 3232 & 6464 \\\newline\hline\newline\end{tabular}\newlineIf this pattern continues, what will be the population of mice in Month 1212?\newlineA. 192192\newlineB. 44,096096\newlineC. 88,192192\newlineD. 1616,384384
  1. Identify Population Growth Pattern: Step 11: Identify the pattern in the population growth.\newlineThe population doubles every month. This is a geometric sequence where each term is twice the previous term.\newlineCalculation: Population at Month 1=81 = 8 (which is 4×24 \times 2), Population at Month 2=162 = 16 (which is 8×28 \times 2), and so on.
  2. Predict Population at Month 1212: Step 22: Use the pattern to predict the population at Month 1212.\newlineSince the population doubles each month, the population at Month 1212 will be 44 (initial population) multiplied by 22 raised to the power of 1212 (since there are 1212 months).\newlineCalculation: 4×2124 \times 2^{12}
  3. Calculate 2122^{12}: Step 33: Calculate 2122^{12}. 212=40962^{12} = 4096
  4. Multiply by Initial Population: Step 44: Multiply the result by the initial population.\newlineCalculation: 4×4096=163844 \times 4096 = 16384

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