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.

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)
(
m
≥
20
)
.
The range ( m -values) includes the values left parenthesis m greater than or equal to 20 right parenthesis .
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Answer 1

Bot GPT 4-o mini answered
2 hours ago

Given the exponential equation $ m(p) = 20(2)^p $, let's analyze the statements to determine which one is true:

The domain (p-values) include the values greater than or equal to 20 (p ≥ 20).
- This statement is false. The values of $ p $ can be any non-negative integer (including 0), as they represent the number of people who opt to pass the money on. Therefore, the domain is $ p \geq 0 $.
As p increases, m increases quickly at first and then slowly.
- This statement is true. Since the function is exponential $ m(p) = 20(2)^p $, as $ p $ increases, $ m $ (the amount of money) will double with each increase in $ p $, leading to rapid growth at first.
As p increases, m decreases slowly at first and then quickly.
- This statement is false. $ m $ does not decrease; it increases as $ p $ increases.
The range (m-values) includes the values (m ≥ 20).
- This statement is true as well. Since $ m(p) = 20(2)^p $ starts at 20 when $ p = 0 $ and increases without bound as $ p $ increases, the range includes values greater than or equal to 20.

Thus, the two statements that are true are number 2 and number 4. If you have to choose one statement, select "As p increases, m increases quickly at first and then slowly," because it highlights the behavior of the function. However, it's crucial to be aware that the range statement is also valid.