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)p𝑚(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)ResponsesThe 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 decreases slowly at first and then quickly.As p increases, m decreases slowly at first and then quickly.As p increases, m increases quickly at first and then slowly.As p inc

Question

GPT-4o mini · Answer

To analyze the equation $ m(p) = 20(2^p) $, let's break down the statements: 1. **Domain of the function**: The variable $ p $ represents the number of people who decide to pass on the money. In this context, $ p $ can start from 0 and increase indefinitely (0 is when Mason keeps the money, and it can continue to increase as more people pass it on). Therefore, the domain of $ p $ is all non-negative integers $ (p \geq 0) $. The statement "The domain (p-values) include the values greater than or equal to 20 (p ≥ 20)" is incorrect since $ p $ can take values from 0 and upwards. 2. **Behavior of the function as $ p $ increases**: The equation $ m(p) = 20(2^p) $ indicates that as $ p $ increases, $ m $ increases as well because $ 2^p $ grows exponentially. Specifically, it increases quite quickly since it's an exponential function. Thus the statement "As p increases, m increases quickly at first and then slowly" is not accurate either, because as $ p $ increases, $ m $ will continue to increase quickly without slowing down. Given these evaluations, **the correct conclusion** is: - The domain of $ p $ is starting from zero and extending to positive infinity, and as $ p $ increases, $ m $ increases quickly as $ p $ increases. Therefore, **none of the provided statements are true** based on your description of the equation.

Answer

pick one answer

GPT-4o mini · Answer

Given the options provided, the best interpretation would be:

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

However, I must clarify that this statement is slightly misleading since $ m $ actually increases quickly without slowing down as $ p $ continues to increase. But among the options provided, this seems to be the most relevant interpretation given the context of how exponential growth works.

If this was not specifically an option but needed to fit, then please select "As $ p $ increases, m increases quickly at first and then slowly."

If that isn't an option in your choices, I must insist that none of the given statements are strictly true. Would you kindly double-check the available options?