Suppose a population of insects quadruples every 6 months an

Suppose a population of insects quadruples every 6 months, and e is the 1-month growth factor. a. Which of the following are equal to the 6-month growth factor? Choose all that apply. a^6 6c c 4c 6 c^1/4 4 c^1/6 c^4 b. Use your results above to find the 1-month growth factor. e = c. Find the 1-year growth factor. d. Find the 1-day growth factor.

Solution

(a) Let c be the one months growth factor, then and if initial population of insects be a, then

Population after one month = a.c,   Population after four months = a.c⁴

Population after two months = a.c² Population after two months = a.c⁵

Population after three months = a.c³   Population after two months = a.c⁶

(b)   The population, using Six months growth factor for the population of bacteria = 4 a

Thus, a c⁶ = 4 a or,    c = 4^1/6

(c) Let y be the one year growth factor, then population after 1 year will be

= a.y, where a is the initial population of the insects

Population of insects at the end of first six month  = (4 a), and

Population of insects at the end of second six month (i.e. after i year) = 4 (4 a) = 16 a

Thus, ay = 16 a => y = 16

  (d) Taking 1 month = 30 days, if d be the one day growth factor, and if initial population of insects be a, then

the population of insects after 30 days = a d³⁰ = a c = a c => d = 4^1/180 = 0.0056