Final answer:
To find the initial bacterial population with a doubling time of 15 minutes and an observed population of 60,000 after 90 minutes, we reverse the doubling process six times to estimate an initial population of approximately 938 bacteria. Using this initial figure and assuming exponential growth without constraints, we can then predict the population after 5 hours by applying twenty doublings.
Step-by-step explanation:
The question is asking to calculate the initial bacterial population, given that its doubling time is 15 minutes and that after 90 minutes the population was 60,000. To solve this, we determine how many doubling periods fit within 90 minutes. Since there are 6 doublings in 90 minutes (90 divided by 15), we can calculate the initial population by dividing 60,000 by 2 six times:
60,000 / 26 = 60,000 / 64 = 937.5
Rounded to the nearest whole number, there were approximately 938 bacteria to start with.
After 5 hours, or 300 minutes, which equals 20 doublings (300 divided by 15), the population would be:
Initial population × 220 = 938 × 220
Assuming no limits on growth. This leads to a significantly larger number of bacteria after 5 hours.