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Question

An increasing curve with an arrow on the upper end is plotted on a coordinate plane. The x-axis is labeled people and ranges from 0 to 5 in increments of 1. The y-axis is labeled money and ranges from 0 to 500 in increments of 100.

Mason is completing a study for his psychology course. For the study, he begins with $20 and asks individuals on the street if they want the money or if they would like him to double it and give it to the next person. He continues to do this until someone takes the money. This situation can be modeled by the exponential equation m(p)=20(2)p
, where m is the money and p is the number of people who opt to pass it on to the next person. Which of the following statements is true about the equation?

(1 point)
Responses

The range (m-values) includes the values (m≥20)
.
The range ( m -values) includes the values left parenthesis m greater than or equal to 20 right parenthesis .

The domain (p-values) include the values greater than or equal to 20 (p≥20)
.
The domain ( p -values) include the values greater than or equal to 20 left parenthesis p greater than or equal to 20 right parenthesis .

As p increases, m increases quickly at first and then slowly.
As p increases, m increases quickly at first and then slowly.

As p increases, m decreases slowly at first and then quickly.
As p increases, m decreases slowly at first and then quickly.
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Answer 1

The correct statement about the equation \( m(p) = 20(2^p) \) is:

As p increases, m increases quickly at first and then slowly.

This is because the function represents exponential growth, where the money \( m \) will increase rapidly as the number of people \( p \) that pass on the money increases. Initially, when \( p \) is small, doubling the amount results in significant increases in the total amount of money; however, with larger values of \( p \), the rate of increase will start to slow down in perceived value compared to the massive increases at smaller values of \( p \).