A mice population doubles every 3 weeks .There are currently 102 mice in a restricted area . If t represents the time in weeks and P(t) is the population of mice , how many mice are there in 105 days?

Answer 1

Make a table! We know that at time "0" there were 102 mice (what we started with), and we know that every 21 days (= 3 weeks) the number of mice doubles. So, after 21 days there are now 102*2=204 mice. Then after 42 days there are 204*2=408 mice

time (days) | # of mice

0 | 102

21 | 204

42 | 408

63 | 816

84 | 1632

105 | 3264

Answer 2

P(t) = 102 * 2^(t/3)

105/7 = 15 weeks

P(15) = 102 * 2^(15/3) = 102 * 2^5 = 3264