The cells of a certain culture of bacteria double every 6 minutes. If the culture contains 100 cells in the beginning, then the total number of cells P in this culture after t minutes is given by the exponential equation P = 100 (2) t/6. Identify the number of minutes it will take for the number of cells to exceed 50,000.

A) 53 min

B) 49 min

C) 48 min

D) 54 min

Since the growth is exponential, therefore I believe the correct form of the equation is:

P = 100 (2) ^ (t / 6)

Where t / 6 is the exponent of 2

So to find for the amount of time needed to exceed the population of 50,000, all we have to do is to plug in that value in the equation and find for t. Therefore:

P = 100 (2) ^ (t / 6)

50000 = 100 (2) ^ (t / 6)

500 = 2^ (t / 6)

log 500 = (t / 6) log 2

t / 6 = log 500 / log 2

t = 6 * 8.96578

t = 53.8 mins = 54 mins

Answer:

D. 54 min