If a certain bacteria doubles in number every 30 minutes, how many bacteria will

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Question: If a certain bacteria doubles in number every 30 minutes, how many bacteria will there be after 2 hours if you start with 100 bacteria?

Options:

Correct Answer: 1600

Solution:

In 2 hours, there are 4 doubling periods (2 hours / 0.5 hours). Number of bacteria = 100 * 2^4 = 100 * 16 = 1600.

If a certain bacteria doubles in number every 30 minutes, how many bacteria will there be after 2 hours if you start with 100 bacteria?

If a certain bacteria doubles in number every 30 minutes, how many bacteria will there be after 2 hours if you start with 100 bacteria?

Step 1: Start with the initial number of bacteria, which is 100.
Step 2: Determine how long you are observing the bacteria, which is 2 hours.
Step 3: Convert 2 hours into minutes: 2 hours = 120 minutes.
Step 4: Find out how many 30-minute periods are in 120 minutes: 120 minutes / 30 minutes = 4 periods.
Step 5: Each period, the number of bacteria doubles. So, after 4 periods, the bacteria will have doubled 4 times.
Step 6: Calculate the total number of bacteria after 4 doublings: Use the formula 100 * 2^4.
Step 7: Calculate 2^4, which is 16.
Step 8: Multiply 100 by 16 to get the final number of bacteria: 100 * 16 = 1600.

Exponential Growth – Understanding how populations grow exponentially, specifically how to calculate the number of organisms after a series of doubling periods.
Time Management – Calculating the number of doubling periods based on the total time given.
Basic Arithmetic – Performing multiplication and exponentiation correctly to find the final number of bacteria.