Answer to Question #159139 in Algebra for Jan

Question

An ant colony triples in number every month. Currently, there are 24 000 in the nest.

a) What is the monthly growth rate of the colony? What is the initial population?

b) Write an equation that models the number of ants in the colony, given the number of months.

c) Use your equation to predict the size of the colony in three months.

d) Use your equation to predict the size of the colony five months ago.

Answer 1

1) 300%; ≈ 11 ants

2) y = $x*3^n$

y - number of ants

x - initial population

n - number of months

3) y = $24000 * 3^3 = 24000 * 27 = 648000$ or $648*10^3$ ants

4) y = $24000 *3^{-5} = 24000/3^5 = 24000 /243 ≈ 98.7 ≈99$ ants