To determine how many bacteria will exist after 2 hours (120 minutes) of real time have passed, you need to follow several steps:
1. Understand the Time Conversion: First, since 1 second of video time corresponds to 20 minutes of real time, you should convert the real time passed into video time.
2. Calculate Video Time: Convert 120 minutes of real time into video time. Since 1 second of video time corresponds to 20 minutes of real time, you can determine the amount of video time that passed by multiplying the real time by the conversion factor between real time and video time.
3. Consider Bacteria Growth Model: Next, identify the bacteria growth model you're working with. Typically for such problems, we use an exponential growth model where bacteria double at regular intervals.
4. Determine Doubling Intervals: Determine the rate at which bacteria double (for example, every 20 minutes). Calculate the number of doubling intervals that fit into the passed real time of 120 minutes.
5. Initial Bacteria Count: Establish the initial count of bacteria. Usually, this problem might start with a single bacterium.
6. Apply the Growth Model: Using the number of doubling intervals calculated, apply the bacteria growth model. If bacteria double every 20 minutes, calculate how many times they have doubled in 120 minutes.
Example Calculation:
1. Conversion to Video Time:
120 minutes of real time corresponds to how many seconds of video time.
Here, 20 minutes of real time equals 1 second of video time, so:
[tex]\( \text{Video time passed} = 120 \, \text{minutes} \times \left( \frac{1 \, \text{second}}{20 \, \text{minutes}} \right) = 6 \, \text{seconds} \)[/tex]
2. Determine Bacteria Growth Rate:
Assume bacteria double every 20 minutes.
3. Number of Doubling Intervals:
In 120 minutes of real time, bacteria will have doubled:
[tex]\( 120 \, \text{minutes} / 20 \, \text{minutes per doubling interval} = 6 \, \text{doublings} \)[/tex]
4. Initial Bacteria Count:
Suppose you start with 1 bacterium.
5. Final Count After Doubling:
After 6 doublings, the bacteria count would be:
[tex]\( \text{Initial count} \times 2^6 = 1 \times 64 = 64 \)[/tex]
So, after 2 hours (120 minutes) have passed, there would be 64 bacteria.
