growth and decay

Question

1. A biologist has 500 cells in a culture at the start of an experiment.  Hourly readings indicated that the number of cells is doubling every hour.
   1. How many cells are present at the end of 4 hours?

 

1. At the end of how many hours are 32,000 cells present?

 

1. Justify your solution.

Answer 1

After 1 hr, the number of cells is 1000; after two hours there will be 2000; after 3 hours 4000; and after 4 hours 8000.

The growth formula is f(t)=500*2^t, where t is the time in hours. When t=4, we have 16*500=8000, as we've seen.

The growth to 32,000 cells is 32000/500=64=2^6, so t=6 hours.