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

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 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 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.

The range (m-values) includes the values (m≥20)
(
𝑚
≥
20
)
.
Th

GPT-4o mini · Answer

To analyze the equation $ m(p) = 20(2)^p $, let's break down the statements provided. 1. **The domain (p-values) include the values greater than or equal to 20 (p ≥ 20):** - This statement is incorrect. The variable $ p $ represents the number of people who opt to pass the money on, which can be any non-negative integer (0, 1, 2, ...). Therefore, the domain is $ p \geq 0 $. 2. **As p increases, m increases quickly at first and then slowly:** - This statement is true. The function $ 20(2)^p $ is an exponential function. Initially, with smaller values of $ p $, the increases in $ m $ are relatively small. However, as $ p $ gets larger, the value of $ m $ grows very quickly because exponential functions increase rapidly. 3. **The range (m-values) includes the values (m ≥ 20):** - This statement is also true. When $ p = 0 $, $ m(0) = 20(2)^0 = 20 $. As $ p $ increases, $ m(p) $ continues to grow larger than 20, so the range of $ m $ is $ m \geq 20 $. In summary, of the statements provided, the second and third statements about the function $ m(p) $ are the true ones, with the most relevant being: - **As p increases, m increases quickly at first and then slowly.**