Question

Use the image to answer the question.

An increasing curve with an arrow on the upper end is plotted on a coordinate plane. The x-axis is labeled people and ranges from 0 to 5 in increments of 1. The y-axis is labeled money and ranges from 0 to 500 in increments of 100.
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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

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

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 .

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

Answer 1

The true statement is: The range (m-values) includes the values m ≥ 20.

Reason: m(p) = 20·2^p and for p = 0 we get m = 20; for any p ≥ 0, 2^p ≥ 1 so m ≥ 20. The other statements are false.