You're a big fan of a new reality series, "Singing Celebration." Contestants from around the country compete to be celebrated as the best singer. Scores are ranked highest to lowest. Those singers falling in the lowest half of the rankings are eliminated. The first season started with 64 contestants. If half of the contestants are eliminated each week, for how many weeks will the program air? Producers have already decided that next season will be 4 weeks longer than this season. How many more contestants will next season need to start with?

 

How many contestants did the show start with in its first season?

How many contestants are eliminated each week? (Ex. in a table)

What equation can be written to find the number of weeks the program airs?

How many weeks will the show's first season air?

How many more weeks will the show's second season air?

How many weeks will the show's second season air?

What equation can be written to find the number of contestants needed or the second season?

How many contestants will the second season start out with?

How many more contestants will the show's second season have than its first season?

Answer:.

1.     The reality T.V. show starts with 64 contestants in the first season.

2.     Table is given below in the explanation

3.     The equation to find the number of weeks is 64/2^x = 1

4.     The first season will air for 6 weeks.

5.     The second season will air for 4 more weeks.

6.     The second season of the show will air for 10 weeks.

7.     The equation for the number of contestants needed for the second season is N/2^x = 1

8.     The second season will start with 1024 contestants.

9.     The second season will have 960 more contestants.

The reality T.V. show starts with 64 contestants in the first season.

As, half of the participants are eliminated after each round so only half of the contestants will remain after the each week that is,

Let x be the number of weeks the program will air then after x weeks we will have 1 winner and in each round the number of contestants left will half, that is,

64/2^x = 1

The first season of the show will air for 6 weeks.

The second season will air for 4 more weeks than season 1.

The second season of the show will air for 6 + 4 weeks that is 10 weeks.

Let the number of contestants in the 2^nd season be N and let the number of season be x then we have,

N/2^x = 1

The second season will air for 10 weeks so we have,

N/2¹⁰ = 1

N = 2¹⁰

N = 1024

Hence the second season will have 1024 contestants.

The second season show will start with 1024 - 64 = 960 more contestants.

PFA