Final answer:
To reach one million amoebae by splitting every half hour, it would take 20 doubling times or 10 hours. The exponential growth formula N = No × 2^n helps to find the number of half-hours required for the amoeba population to reach one million.
Step-by-step explanation:
The question revolves around understanding the concept of exponential growth, specifically in a biological context with amoebae replication. If an amoeba splits into 2 every half hour, the amount replicates exponentially. Therefore, after 1 hour, there would be 4 amoebae (22), and after 2 hours, there would be 16 amoebae (24), given that it doubles every half hour.
To find out when it will reach one million (106) amoebae, we need to figure out how many half-hours it takes for the initial amoeba to replicate to reach a million. The formula for exponential growth is N = N0 × 2n, where N is the final number of amoebae, N0 is the initial number (which is 1 in this case), and n is the number of generations or doubling times. To reach one million, we need to solve for n in 106 = 1 × 2n. By employing the logarithm, we can find that n is approximately 20. Therefore, since n is the number of half-hour intervals, it would take 20 half-hours or 10 hours (since 20 half-hours is equal to 10 full hours) for the number of amoebae to reach one million.
The correct answer is (a) 10 hours.