Use the image to answer the question.

Question

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

Answer 1

To analyze the equation \( m(p) = 20(2)^p \):

1. Understanding the function:

   • The variable \( p \) represents the number of people who choose to pass the money on.
   • The function calculates the amount of money \( m \) based on how many people have passed the money.

2. Domain of the function:

   • \( p \) can be any non-negative integer because you can't have a negative number of people passing on the money. Thus, the domain is \( p \geq 0 \).

3. Range of the function:

   • When \( p = 0 \), \( m(0) = 20 \).
   • As \( p \) increases, \( m(p) \) increases exponentially. There are no upper bounds, so \( m \) can take any value greater than or equal to 20. Thus, the range is \( m \geq 20 \).

Based on the analysis, the correct statement is:

The range (\( m \)-values) includes the values \( m \geq 20 \).