Question

This exercise uses the population growth model. An infectious strain of bacteria increases in number at a relative growth rate of 200 % per hour. When a certain critical number of bacteria are present in the bloodstream, a person becomes ill. If a single bacterium infects a person, the critical level is reached in 24 hours. How long will it take for the critical level to be reached if the same person is infected with 10 bacteria?

Answer 1

It will take 24 hours for the critical level to be reached if the same person is infected with 10 bacteria.

Step-by-step explanation:

To find out how long it will take for the critical level to be reached if the same person is infected with 10 bacteria, we need to calculate the number of hours it takes for the population to reach the critical level. The bacteria population increases at a relative growth rate of 200% per hour. So, for each hour, the population doubles.

Since we know that it takes 24 hours for a single bacterium to reach the critical level, we can use this information to find out how many doubling cycles it takes for the population to reach the critical level.

Let's calculate:

1. After 1 hour: 10 bacteria * 2 = 20 bacteria
2. After 2 hours: 20 bacteria * 2 = 40 bacteria
3. After 3 hours: 40 bacteria * 2 = 80 bacteria
4. ...
5. After 24 hours: 10 bacteria * 2^24 = 16,777,216 bacteria.

So, it will take 24 hours for the critical level to be reached if the same person is infected with 10 bacteria.