Suppose that there are 12,000 bacteria in a colony. An antibiotic is introduced into to kill the colony exponentially. One minute later, there were 9960 bacteria left in the colony.

1. How many bacteria remain in the colony three minutes after the pathogen was introduced? 2. Write a function that can be used to predict the population as a function of minutes. Define your variables. 3. Write a sentence to describe the growth rate.4. Find the size of the colony 11 minutes after the pathogen was introduced? 5. How long will it take for two-thirds of the bacteria to die? 6. When will the bacteria be essentially destroyed? I also need a table for the first 6 minutes after the pathogen was introduced. Thank you!