Question

A singing contest eliminates contestants after each round. The number of contestants that go into round n is equal to the number of contestants in the previous round raised to the n-1/n ​-th ​power, rounded to the nearest integer. The number of contestants in Round 2 is 243. How many contestants will be in Round​ 5?

Answer 1

9514 1404 393

Answer:

9

Explanation:

It is convenient to let a graphing calculator or spreadsheet do the arithmetic.

Into round 3:

243^(2/3) ≈ 38.94, rounds to 39

Into round 4:

39^(3/4) ≈ 15.61, rounds to 16

Into round 5:

16^(4/5) ≈ 9.19, rounds to 9

9 contestants will be in round 5.