50,000 contestants participate in an on-line game. The game randomly eliminates 20% of the contestants each day. Determine the number of contestants remaining in the game after one week.

Answer:10,486 contestants

Step-by-step explanation:

First day:

Total number of contestants at the beginning = 50,000

After first day, 20% 0f 50,000 are removed.

That is, (20/100) * 50,000 = 10,000

Contestants remaining after first day = 50,000-10,000 = 40,000

Second day:

Contestants = 40,000

20% removed

That is (20/100) * 40000=8000

Balance = 40000-8000=32,000

Third day:

Contestants = 32000

20% removed

That is (20/100) * 32000=6400

Balance = 32000-6400=25,600

Fouth day:

Contestants = 25,600

20% removed

That is (20/100) * 25,600=5,120

Balance = 25,600-5,120=20,480

Fifth day:

Contestants = 20,480

20% removed

That is (20/100) * 20,480=4096

Balance = 20,480-4096=16,384

Sixth day:

Contestants = 16,384

20% removed

That is (20/100) * 16,384=3276.8

Balance = 16,384-3276.8=13,107.2

Seventh day:

Contestants = 13,107.2

20% removed

That is (20/100) * 13,107.2=2621.44

Balance = 13107.2-2621.44=10485.76

Therefore, number of contestants remaining after one week equals 10,486.