Question

A certain cell culture has a doubling time of 4 hours. Initially, there were 2000 cells present. Assuming an exponential growth law, determine the time it takes for the culture to contain 10^6 cells.

a. 8 hours
b. 12 hours
c. 16 hours
d. 20 hours

Answer 1

To determine the time it takes for the culture to contain 10^6 cells given a doubling time of 4 hours and an initial cell count of 2000, we can calculate the number of doubling times and multiply it by the doubling time.

Step-by-step explanation:

To determine the time it takes for the culture to contain 10^6 cells, we need to calculate the number of doubling times it would take to reach that number. Since the cell culture has a doubling time of 4 hours, we can use the formula n = (log(N) - log(N0)) / log(2), where n is the number of doubling times, N is the final number of cells, and N0 is the initial number of cells. Plugging in the values, we get n = (log(10^6) - log(2000)) / log(2). Solving this equation, we find that n is approximately 5. Once we have the number of doubling times, we can multiply it by the doubling time to get the total time. Therefore, the time it takes for the culture to contain 10^6 cells is 5 * 4 = 20 hours.