Use the image to answer the 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 , 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) . The domain ( p -values) include the values greater than or equal to 20 left parenthesis p greater than or equal to 20 right parenthesis . 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 . 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 increases, m increases quickly at first and then slowly. Skip to navigation

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GPT-4o mini · Answer

To analyze the equation $ m(p) = 20(2)^p $, we can break down the statements provided: 1. **Domain (p-values)**: The values for $ p $ represent the number of people who opt to pass on the money. Since individuals can either take the money or pass it on, $ p $ must be a non-negative integer (e.g., 0, 1, 2, ...). Therefore, the domain is $ p \geq 0 $, not $ p \geq 20 $. 2. **Range (m-values)**: The value of $ m $ starts at $ 20(2)^0 = 20 $ when $ p = 0 $ and increases as $ p $ increases. As $ p $ approaches infinity, $ m $ will also approach infinity. Hence, the range is $ m \geq 20 $. 3. **Behavior of m as p increases**: Based on the equation, as $ p $ increases, $ m $ increases exponentially. Therefore, as $ p $ increases, $ m $ increases quickly at first and then continues to increase, but it never decreases. Considering the analysis above, the true statement is: - **The range (m-values) includes the values (m ≥ 20)**.