Explanation:
To find the doubling period of a bacteria culture, we can use the formula:
Doubling period = (time2 - time1) * log(2) / log(population2 / population1)
In this case, the count in the bacteria culture was 800 after 20 minutes and 1200 after 40 minutes. Let's plug these values into the formula:
Doubling period = (40 - 20) * log(2) / log(1200 / 800)
Doubling period = 20 * log(2) / log(1.5)
Using a calculator, we find that the doubling period is approximately 10.3 minutes.
To find the population after 95 minutes, we can use the formula:
Population after time = initial population * (2 ^ (time / doubling period))
Using the given initial population of 800 and the calculated doubling period of 10.3 minutes, we can find the population after 95 minutes:
Population after 95 minutes = 800 * (2 ^ (95 / 10.3))
Using a calculator, we find that the population after 95 minutes is approximately 28428.
To find when the population will reach 10000, we can rearrange the formula:
time = doubling period * log(population / initial population) / log(2)
Using the given initial population of 800 and the target population of 10000, we can find the time it takes for the population to reach 10000:
time = 10.3 * log(10000 / 800) / log(2)
Using a calculator, we find that it takes approximately 108.9 minutes for the population to reach 10000.
It's important to note that these calculations assume exponential growth and may not hold true for all types of bacteria cultures. Additionally, real-life conditions can affect the growth rate