Acertain insect population doubles every 3 days. suppose that currently, there are 50 insects in the colony. how many insects will be in the colony in 3 weeks. a- 1600 b- 6400 c- 3200 d- 12800

This is exponential growth.  We start with 50 insects.  In 3 days we have 100 insects (double 50).  Therefore,

100 = 50*e^(k*3), where k is the growth constant.
                                                                        log 2
Then 2 = e^(3k), and log 2 = 3k, so that k =
                                                                           3
                                  log 2
Formula:  N = 50*e{ *t}
                                     3

You'll need to evaluate this formula for t=3 (weeks).  Can you do that?