Final answer:
The bacterial culture that triples every 2 minutes will surpass 9500 cells just after 10 minutes. Since we cannot have a fraction of a minute in this context, the answer is 11 minutes (Option C).
Step-by-step explanation:
The student is asking about exponential growth, specifically in a bacterial culture that triples every 2 minutes. To find out how many minutes it will take for the initial 40 cells to grow to more than 9500, we can use the formula for exponential growth:
N = N0 × 3t/2
Where N is the final number of cells, N0 is the initial number of cells (40 in this case), and t is the time in minutes.
We want N to be greater than 9500, so we solve the inequality:
9500 < 40 × 3t/2
Dividing both sides by 40 gives:
237.5 < 3t/2
Next, we find the smallest t for which the inequality holds by applying logarithms and solving:
t > 2 × (log3(237.5))
Calculating the right side, we get:
t > 10.096
So, the culture will have more than 9500 cells just after 10 minutes. The smallest whole number of minutes greater than 10.096 is 11, hence the answer is: C) 11 min