The amount of time it takes for Bacteria X to complete binary fission is 15 minutes. a. Doubling Time for Bacteria X = ? b. How many bacteria are present after that amount of time?
Understand the Problem
The question is asking for the doubling time of Bacteria X and how many bacteria are present after a specific amount of time, which is given as 15 minutes for binary fission.
Answer
a. 15 minutes; b. 2 bacteria
Answer for screen readers
a. Doubling Time for Bacteria X = 15 minutes
b. Number of bacteria present after 15 minutes = 2
Steps to Solve
- Understanding Doubling Time
The doubling time of a bacterium during binary fission is the same as the time taken for it to divide. In this case, since Bacteria X takes 15 minutes to complete one binary fission, the doubling time is 15 minutes.
- Calculating the Number of Bacteria After Given Time
To determine how many bacteria are present after one doubling (15 minutes), we can use this formula: If we start with one bacterium, after one doubling: $$ \text{Number of bacteria} = 2^n $$ where ( n ) is the number of doublings.
Since ( n = 1 ) after 15 minutes, the calculation is: $$ \text{Number of bacteria} = 2^1 = 2 $$
- Summary of Findings
- a. Doubling Time for Bacteria X = 15 minutes
- b. After 15 minutes, there are 2 bacteria.
a. Doubling Time for Bacteria X = 15 minutes
b. Number of bacteria present after 15 minutes = 2
More Information
Bacteria reproduce by a process called binary fission, where one bacterium splits into two. Each doubling time, the population of bacteria doubles.
Tips
- Confusing the doubling time with the total time. Always remember that the doubling time is the time for the population to double, not the total duration of observation.
- Forgetting to apply the exponential growth formula correctly. Ensure to use (2^n) where (n) is the number of times doubling occurs.
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