Question

The population of a colony of beetles grows 30% each week. If the initial population is 65 beetles, how many beetles will be there after 5 weeks

Answer 1

This is question of geometric sequence, equation of growth for this matter. The explicit formula for geometric sequence is given by:

a(n) = a(0)r^(n-1)

where;
a(n) = population after time "n"
a(0) = Initial population = 65
n = time = 5 weeks
r = common ratio = (100+30)% = 1.3

Substituting, beetles after 5 weeks will be;
a(5) = 65*1.3^(5-1) = 185.65 ≈ 186 beetles