Hal's racquet club sponsors an annual racquetball tournament. The tournament starts with 124 participants. After each round, half of the players are eliminated.

The number of players remaining after 9 rounds can be represented by which of the following types of functions?

linear
quadratic
exponential decay
exponential growth

@ganeshie8 @tkhunny @jim_thompson5910

Question

Hal's racquet club sponsors an annual racquetball tournament. The tournament starts with 124 participants. After each round, half of the players are eliminated.

The number of players remaining after 9 rounds can be represented by which of the following types of functions?

linear
quadratic
exponential decay
exponential growth

@ganeshie8 @tkhunny @jim_thompson5910

jim_thompson5910 · Answer

your thoughts?

anonymous · Answer

Can you give me an example of each? @jim_thompson5910

jim_thompson5910 · Answer

How many people do we start with?

anonymous · Answer

@jim_thompson5910 124

jim_thompson5910 · Answer

how many people get eliminated?

jim_thompson5910 · Answer

after that first round

anonymous · Answer

62

jim_thompson5910 · Answer

so 62 are leftover

how many are eliminated after round 2?

anonymous · Answer

My question just timed out, but 31.

jim_thompson5910 · Answer

ok, we'll keep going anyways

the idea is that each time you cut each term in half to get the next term

124, 62, 31, etc etc

this is a geometric sequence and the nth term is

$$\Large a_{n} = 124(1/2)^{n-1}$$

jim_thompson5910 · Answer

you can rewrite this as a function 

$$\Large f(x) = 124(1/2)^{x-1}$$

where it only makes sense to have x be an integer and be a positive number

jim_thompson5910 · Answer

what kind of function did I just write?