Question

Two thousand mosquitoes are placed in a glass container into which an insecticide is sprayed. If the number of mosquitoes still alive decreases by 75% every two hours, approximately how many mosquitoes will be alive 6 hours after they were originally placed into the container?

A) 13
B) 844
C) 32
D) 27
E) 0

Answer 1

After 6 hours, the mosquito population would be reduced from 2000 to approximately 31 mosquitoes. This is calculated by reducing the population by 75% every 2 hours, three times.

Step-by-step explanation:

The student is asking how many mosquitoes will be alive after 6 hours if 2000 mosquitoes are exposed to an insecticide that reduces the population by 75% every 2 hours. To solve this problem, we calculate the number of mosquitoes after each interval.

Initial population: 2000 mosquitoes

After 2 hours: 2000 × 0.25 = 500 mosquitoes

After 4 hours: 500 × 0.25 = 125 mosquitoes

After 6 hours: 125 × 0.25 = 31.25 mosquitoes

Since we can't have a fraction of a mosquito, we round down to 31 mosquitoes, which matches answer choice D).