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Question 1185401: Shreya is very interested in cryogenics (the science of very low temperatures). With the help of her science teacher she is doing an experiment on the effect of low temperatures on bacteria. She cools one sample of bacteria to a temperature of -51°C, another to -45oC, a third to -81oC, and finally another to -76°C. What was the temperature difference in the two coldest experiments? Each experiment began with 12 individual bacteria, and the strain of cold resistant bacteria she was testing stopped growing at -47oC, and they doubled each minute. Further, the bacteria started to die off at 75oC, losing ⅓ of the colony each minute. How many bacteria will Shreya have at the end of the third experiment if she began the experiment at 13oC, and it takes 15 seconds to increase or decrease the temperature by 1 degree?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to break down this problem:
1. **Temperature Difference:** The two coldest temperatures are -81°C and -76°C. The difference between them is |-81 - (-76)| = |-81 + 76| = |-5| = 5°C.
2. **Bacteria Growth (Irrelevant to the question asked):** The information about the bacteria doubling and dying off, and the temperature at which they stop growing or start dying is extra information and not needed to answer the temperature difference question.
3. **Bacteria in the third experiment:**
* **Initial Temperature:** 13°C
* **Target Temperature:** -81°C
* **Temperature Difference:** 13 - (-81) = 94°C
* **Time to cool:** 94°C * 15 seconds/°C = 1410 seconds
* **Minutes to cool:** 1410 seconds / 60 seconds/minute = 23.5 minutes
Since the bacteria stop growing at -47°C, we need to determine how long it takes to reach that temperature:
* Temperature difference to reach -47°C: 13 - (-47) = 60°C
* Time to reach -47°C: 60°C * 15 seconds/°C = 900 seconds = 15 minutes.
For the first 15 minutes, the bacteria doubles every minute. So, after 15 minutes, the number of bacteria will be 12 * 2^15 = 393216.
The bacteria stops growing at -47°C. The experiment cools to -81°C, which is much lower, so the bacteria will not grow beyond that point. The time to reach -81°C is 23.5 minutes, but the bacteria count will be the same as after 15 minutes because the bacteria stop growing at -47°C.
Therefore, Shreya will have 393,216 bacteria at the end of the third experiment.
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