Question

There were 816 people at a concert when a band started playing. After each song, only half of the people stayed to hear the next song. How many people were left at the concert after x songs? Write a function to represent this
scenario.

Answer 1

To represent the scenario of people leaving a concert after each song, you can create a function that models the number of people remaining after each song.

Initially, there are 816 people at the concert. After each song, only half of the people stay for the next song. This can be expressed mathematically as follows:

- Let \( P(x) \) be the number of people left after \( x \) songs.
- The initial number of people is \( P(0) = 816 \).
- After the first song, the number of people remaining is \( P(1) = \frac{816}{2} \).
- After the second song, the number of people remaining is \( P(2) = \frac{816}{2^2} \).
- In general, after \( x \) songs, the number of people remaining is \( P(x) = \frac{816}{2^x} \).

Thus, the function \( P(x) \) can be written as:

\[
P(x) = \frac{816}{2^x}
\]

This function will give you the number of people left at the concert after \( x \) songs.