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?

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?

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

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

C) As p increases, m increases quickly at first and then slowly.

D) As p increases, m decreases slowly at first and then quickly.

Answer 1

The correct statement about the equation is:

C) As p increases, m increases quickly at first and then slowly.

This is because the equation is exponential, with a base of 2. As p increases, the value inside the parentheses (2^p) increases rapidly. Therefore, m increases quickly at first. However, as p continues to increase, the rate of increase slows down, resulting in m increasing slowly.