Short Answer 
To determine the cell count after 15 hours, we calculate 5 doubling periods (15 hours ‚àö‚àë 3 hours). Starting with 300,000 cells/mL, the final count becomes 9,600,000 cells/mL after applying the doubling formula (300,000 cells/mL ‚àöo 2^5).
Step 1: Calculate Doubling Periods
To find how many times the cells double in 15 hours, we need to calculate the number of doubling periods. Since the cells double every 3 hours, we perform the following calculation:
- Divide the total time (15 hours) by the doubling time (3 hours).
- This gives us 15 hours ‚àö‚àë 3 hours = 5 doubling periods.
Step 2: Apply the Doubling Formula
Now, we will use the doubling periods to find the final count of cells per milliliter. The formula for calculating the final number of cells based on the initial count and doubling periods is:
- Final number of cells = Initial number of cells ‚àöo 2^(number of doubling periods).
- Here, the initial count is 300,000 cells/mL and you will multiply it by 2 raised to the power of the number of doubling periods (5).
Step 3: Calculate Final Cell Density
We now compute the final cell count using the formula derived earlier. Substituting the values into the equation gives:
- Final number of cells = 300,000 cells/mL ‚àöo 2^5.
- This equals 300,000 cells/mL ‚àöo 32, resulting in a final count of 9,600,000 cells/mL.
Thus, 15 hours after the initial observation, the liquid growth medium will contain approximately 9,600,000 cells per milliliter.