Final answer:
The colony of bacteria will take 2 hours to contain 4,000 bacteria.
Step-by-step explanation:
To determine how many hours it will take for the colony to contain 4,000 bacteria, we need to calculate the number of doubling cycles. Since the colony doubles in size every 30 minutes, there are 2 doubling cycles per hour. We can use the formula N = N0 * 2^n, where N is the final number of bacteria, N0 is the initial number of bacteria, and n is the number of doubling cycles. Let's calculate:
N = 400 * 2^n
4000 = 400 * 2^n
10 = 2^n
n = log2(10)
n = 3.32
Since we can't have a fraction of a doubling cycle, we need to round up to the nearest whole number. Therefore, it will take 4 doubling cycles, which is equivalent to 2 hours, for the colony to contain 4,000 bacteria.