Final answer:
To solve this bacteria growth problem, we calculate the number of doubling times in 8 hours and use the formula N = 2^n to determine the number of bacteria. The correct answer is d) 8192 bacteria.
Step-by-step explanation:
To solve this problem, we need to calculate the number of bacteria at 5:00 PM, eight hours after 9:00 AM. Since the bacteria doubles every 5 minutes, we can determine the number of doubling times in 8 hours by dividing 8 hours by 5 minutes: 8 hours / 5 minutes = 960 minutes / 5 minutes = 192 doubling times.
Starting with one bacterium, after one doubling time we have 2 bacteria, after two doubling times we have 4 bacteria, and so on. We can express the number of bacteria after each doubling time using the formula N = 2^n, where N is the number of bacteria and n is the number of doubling times. Therefore, after 192 doubling times, we have N = 2^192 = 6.2771017 x 10^57 bacteria.
Since none of the answer choices match this value, we round the number to the nearest power of 2, which is 8.192 x 10^57 bacteria. The nearest power of 2 is 2^197 = 7.084 x 10^59 bacteria, which is larger than our calculated value. Therefore, the correct answer is d) 8192 bacteria.