Incubator Alarm and Bacteria Count
During a heat wave, the school's science lab loses power for several hours. A culture of bacteria in a sealed incubator is being monitored for a lab report. The culture starts with 5,000 bacteria at 8:00 a.m., and the lab notes say the population doubles every 20 minutes while the incubator stays between 36.5 °C and 38.0 °C. The incubator begins at 37.0 °C. A student volunteer records these temperature changes from the starting reading: +2.5 °C, −1.75 °C, +3.25 °C, and −0.5 °C. The alarm sounds if the final temperature is outside the safe range. The class must also decide whether to repeat the experiment; their rule is that a run is valid only if the final bacteria count is at least 60,000 after 80 minutes and the temperature stayed in range. The teacher asks for a written conclusion with calculations, not just a yes or no.
1. Calculate the bacteria count after 80 minutes. Show the exponent you use and explain what it represents.
Read the worked answer
The population doubles every 20 minutes, so the number of doublings in 80 minutes is 80 ÷ 20 = 4. The count is 5,000 × 2^4. Since 2^4 = 16, the count is 5,000 × 16 = 80,000 bacteria. The exponent 4 is the number of doubling periods, not the number of minutes. This count meets the 60,000-bacteria requirement for a valid run.
2. Find the final incubator temperature and decide whether the alarm sounds. Show the sum of the changes.
Read the worked answer
Add the recorded changes: +2.5 + (−1.75) = 0.75; 0.75 + 3.25 = 4.0; 4.0 + (−0.5) = 3.5. The net change is +3.5 °C. Starting from 37.0 °C, the final temperature is 37.0 + 3.5 = 40.5 °C. The safe range is 36.5 °C to 38.0 °C, and 40.5 °C is above 38.0 °C, so the alarm sounds.
3. Using both results, write the class's conclusion about whether the run is valid. Explain how the two conditions interact.
Read the worked answer
The bacteria condition is met because 80,000 is at least 60,000. The temperature condition is not met because 40.5 °C is outside 36.5 °C to 38.0 °C. A valid run requires both conditions, so the run is invalid and should be repeated. The high count cannot be trusted as normal growth data because the temperature was not controlled; the class should report that the incubator exceeded the safe range before using the count in the lab report.