Question

The population of locusts in a certain swarm doubles every two hours. If 4 hours ago the swarm just doubled to 1,000 locusts, in approximately how many hours will the swarm population exceed 250,000 locusts?

Answer 1

14 hours

Explanation:

The population of locusts in a certain swarm doubles every two hours.

If 4 hours ago the swarm just doubled to 1,000 locusts.

The population now will be 1000X2X2=4000

This is an example of a geometric progression with

First term, a=4000

Common ration, r=2

We want to determine in how many hours, the population will exceed 250,000.

Nth term of a G.P.

Uₙ=arⁿ⁻¹

arⁿ⁻¹>250000

4000 X 2ⁿ⁻¹ >250000

2ⁿ⁻¹ > 2⁶ > 62.5

n-1>6

n>7

Since an increase occurs every 2 hours, It means that in approximately 14 hours, the population will increase to over 250000.