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?

A. 6
B. 8
C. 10
D. 12
E. 14

Answer 1

6 hours

Explanation:

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

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

So, present population = 4000

Rate = 2

Formula :
`y=ab^x`

y is the population after x hours

a is the present population

b is the rate

`4000 * 2^n = 250,000`

`2^n =62.5`

Taking natural log both sides

`|ln 2^n =|ln 62.5`

`n |ln 2 =|ln 62.5`

`n =(|ln 62.5)/(|ln 2)`

`n =5.9`

n is approximately 6

So, the swarm population exceed 250,000 locusts in 6 hours

So, Option A is true .