Question

After how many hours would the scientists expect to have one million bacterial cells if a bacterial colony grows at a rate such that its population is 10 times what it was 50 hours earlier?

A. 75 hours
B. 100 hours
C. 150 hours
D. 200 hours

Answer 1

To determine after how many hours the scientists would expect to have one million bacterial cells if the population doubles every 5 hours, we can calculate the number of doubling cycles needed to reach that size and multiply it by the doubling time.

Step-by-step explanation:

To determine after how many hours the scientists would expect to have one million bacterial cells, we need to find the doubling time of the bacterial colony. In this case, the population of the colony is 10 times what it was 50 hours earlier. Let's start by finding the number of doubling cycles that occur in 50 hours. If the population is 10 times what it was 50 hours earlier, it means that the population doubles 10 times during that period. Therefore, the doubling time would be 50 hours divided by 10, which is 5 hours.

Now let's calculate how many doublings would occur in order to reach one million cells. Since each doubling takes 5 hours, and we want to reach one million cells, we can set up the equation: 2^(n) = 1,000,000, where n represents the number of doublings. We can solve this equation by taking the logarithm base 2 of both sides: n = log2(1,000,000) ≈ 20.

Therefore, it would take approximately 20 doubling cycles of 5 hours each, or 100 hours, for the bacterial colony to reach one million cells. So, the answer is B. 100 hours.