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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

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.

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)
.

Answer 1

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

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

This is because the equation is exponential in nature, where \( m \) increases exponentially as \( p \) (the number of people who pass it on) increases. Initially, for smaller values of \( p \), the increases in \( m \) are notable, but as \( p \) gets larger, the changes in \( m \) become less perceptible within a limited range but still increase rapidly due to the exponential factor \( (2)^p \).

The other options are incorrect:

• The range does include values \( m \geq 20 \), but it actually continues to include all greater values as \( p \) increases.
• The domain does not start at \( p \geq 20 \); instead, \( p \) can start at 0 (no one has passed it on yet).

Thus, the first statement is the most accurate reflection of the behavior of the function.