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 where the number of people at the concert halves after each song, we can define a function based on the initial number of people and the number of songs.

Let \( P(x) \) represent the number of people left after \( x \) songs. Initially, there are 816 people. After each song, the number of people is halved, which mathematically can be expressed as:

\[
P(x) = 816 \times \left(\frac{1}{2}\right)^x
\]

Here:
- \( P(x) \) is the number of people remaining after \( x \) songs,
- 816 is the initial number of people,
- \( x \) is the number of songs played,
- \( \left(\frac{1}{2}\right)^x \) represents the halving process for each song.

In summary, the function that represents the number of people left at the concert after \( x \) songs is:

\[
P(x) = 816 \times \left(\frac{1}{2}\right)^x
\]