2 Multiple Choice 10 points A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If \( t \) represents the time, in weeks, and \( P(t) \) is the population of rabbits with respect to time, and how many rabbits will there be in 98 days? 152 81,920 3,688 56

To find the population of rabbits after 98 days, we first need to determine the population function \( P(t) \) based on the given information. Given: - The rabbit population doubles every 4 weeks. - There are currently 5 rabbits in the restricted area. Since the population doubles every 4 weeks, we can express the population function as: \[ P(t) = 5 \times 2^{\frac{t}{4}} \] Now, we need to find the population after 98 days. First, we need to convert 98 days to weeks: \[ 98 \text{ days} = \frac{98}{7} \text{ weeks} \] Substitute the value of \( t \) into the population function: \[ P\left(\frac{98}{7}\right) = 5 \times 2^{\frac{98}{7} \div 4} \] Now, we can calculate the population after 98 days. Calculate the value by following steps: - step0: Calculate: \(5\times 2^{\frac{\frac{98}{7}}{4}}\) - step1: Divide the terms: \(5\times 2^{\frac{14}{4}}\) - step2: Reduce the fraction: \(5\times 2^{\frac{7}{2}}\) - step3: Rewrite the expression: \(5\times 8\sqrt{2}\) - step4: Expand the expression: \(40\sqrt{2}\) The population of rabbits after 98 days will be approximately 56.57 rabbits. Therefore, the correct answer is 56.