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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The curve begins approximately at the point left parenthesis 0 comma 20 right parenthesis and passes through the points left parenthesis 1 comma 40 right parenthesis, left parenthesis 2 comma 80 right parenthesis, left parenthesis 3 comma 160 right parenthesis, left parenthesis 4 comma 320 right parenthesis, and left parenthesis 4.5 comma 450 right parenthesis.

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)

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

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

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

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

Answer 1

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

Reason: m(p) = 20·2^p and at p = 0, m = 20; for p ≥ 0 the function grows, so m ≥ 20. (The other statements are false.)