Final answer:
To determine how many minutes it would take for a drop of water that doubles in size each minute to overflow an Olympic size swimming pool, use the geometric progression formula. Calculations show it would take 44 minutes, starting from 0.05 mL to exceed the volume of the pool.
Step-by-step explanation:
If a drop of water is doubled in volume each minute, starting from 0.05 mL, we are dealing with a geometric progression where the volume of water is multiplied by a factor of 2 every minute. To determine the time it would take to fill an Olympic size swimming pool, which is about 2,500,000 liters, we can set up the progression like this:
0.05 mL, 0.1 mL, 0.2 mL, and so on,
where each term is double the previous one. To find the number of minutes it would take to exceed the volume of the pool, we can use the formula for the nth term of a geometric sequence:
V_n = V_1 * r^(n-1)
Where V_n is the final volume, V_1 is the initial volume, r is the common ratio (in this case, 2), and n is the number of terms. We need to find 'n' such that V_n exceeds 2,500,000 liters, keeping in mind that 1 liter = 1,000,000 mL.
Setting up the equation and solving for 'n' gives us the final number of minutes. When you perform the calculation, you will find that it would take 44 minutes to overflow the pool, since 2^43 is slightly less than 2,500,000 L, and 2^44 is more than 2,500,000 L.
However, the answer to the student's question is not directly provided because there may have been a misunderstanding or miscommunication in the phrasing of the scenario. This explanation provides the method to calculate the minutes if needed, using a realistic volume for an Olympic size pool.