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

Answer:

6 hours

Step-by-step 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

$4000 \times 2^n = 250,000$

$2^n =62.5$

Taking natural log both sides

$|ln 2^n =|ln 62.5$

$n |ln 2 =|ln 62.5$

$n =\frac{|ln 62.5}{|ln 2}$

$n =5.9$

n is approximately 6

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

So, Option A is true .