There are 70,000 bacteria present in a culture. An antibiotic is introduced to the culture and the number of bacteria is reduced by half every 4 hours. Which of the following statements are true? Select all that apply.
Two hours after the antibiotic is introduced, there are 35,000 bacteria present in the culture.
24 hours after antibiotic is introduced, the number of bacteria in the culture is reduced to 1093.
The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay.
The half-life of the bacteria after the antibiotic is introduced is 2 hours.
The function B(x) = 70,000(0.5)^x, where x is the number of 4 hour periods, represents the amount of bacteria present after the antibiotic is introduced.
- Two hours after the antibiotic is introduced, there are 35,000 bacteria present in the culture. (True)
- 24 hours after the antibiotic is introduced, the number of bacteria in the culture is reduced to 1093. (True)
- The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay. (True)
- The half-life of the bacteria after the antibiotic is introduced is 2 hours. (True)
- The function B(x) = 70,000(0.5)^x, where x is the number of 4 hour periods, represents the amount of bacteria present after the antibiotic is introduced. (True)
are you sure?
I apologize for the error in my previous response. Let's go through each statement again:
- Two hours after the antibiotic is introduced, there are 35,000 bacteria present in the culture. (False) - Every 4 hours, the number of bacteria is reduced by half. After 2 hours, there would still be 70,000 bacteria present.
- 24 hours after antibiotic is introduced, the number of bacteria in the culture is reduced to 1093. (True) - This is true because every 4 hours, the number of bacteria is reduced by half so after 24 hours there would be 1093 bacteria left.
- The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay. (True) - This is true because the bacteria population is decreasing by a constant percentage over equal periods of time.
- The half-life of the bacteria after the antibiotic is introduced is 2 hours. (False) - The half-life of the bacteria is 4 hours, not 2 hours.
- The function B(x) = 70,000(0.5)^x, where x is the number of 4 hour periods, represents the amount of bacteria present after the antibiotic is introduced. (True) - This is true because the function represents the exponential decay of bacteria population every 4 hours.