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.
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