3. The table below shows the population of a group of mice over a period of time.POPULATION OF MICE\begin{tabular}{|l|c|c|c|c|c|}\hline Month & 0 & 1 & 2 & 3 & 4 \\\hline Population & 4 & 8 & 16 & 32 & 64 \\\hline\end{tabular}If this pattern continues, what will be the population of mice in Month 12?A. 192B. 4,096C. 8,192D. 16,384
Q. 3. The table below shows the population of a group of mice over a period of time.POPULATION OF MICE\begin{tabular}{|l|c|c|c|c|c|}\hline Month & 0 & 1 & 2 & 3 & 4 \\\hline Population & 4 & 8 & 16 & 32 & 64 \\\hline\end{tabular}If this pattern continues, what will be the population of mice in Month 12?A. 192B. 4,096C. 8,192D. 16,384
Identify Population Growth Pattern: Step 1: Identify the pattern in the population growth.The population doubles every month. This is a geometric sequence where each term is twice the previous term.Calculation: Population at Month 1=8 (which is 4×2), Population at Month 2=16 (which is 8×2), and so on.
Predict Population at Month 12: Step 2: Use the pattern to predict the population at Month 12.Since the population doubles each month, the population at Month 12 will be 4 (initial population) multiplied by 2 raised to the power of 12 (since there are 12 months).Calculation: 4×212
Calculate 212: Step 3: Calculate 212. 212=4096
Multiply by Initial Population: Step 4: Multiply the result by the initial population.Calculation: 4×4096=16384