Check Up

In a research lab, an antibiotic is tested by exposing it to a bacteria. Because of the presence of the antibiotic, the number of bacteria in each new generation is \(70\%\) of the number in the previous generation. There were \(24\thinspace 000\) bacteria initially.

1. Find the number of bacteria in the first five generations.
   
   
   
2. Assuming nothing inhibits the growth of bacteria, what is the total number of bacteria in the first five generations?
   
   
   
3. Assuming nothing inhibits the growth of bacteria, has the population reached \(100\thinspace 000\) by the tenth generation?
   
   
   
4. If this growth trend continues indefinitely, how many bacteria will there be in the population?