Question

the scatterplot shows the relationship between x and y for the 10 data points in data set g. data set h is created by multiplying the y-value of each data point from data set g by 20. which of the following equations is the most appropriate model for data set h?
a. ( y = 20(0.30)^x + 20 )
b. ( y = 26(0.30)^x )
c. ( y = 26(0.30)^x + 20 )
d. ( y = 522(0.30)^x )

Explanation:

Step1: Analyze Data Set G's Model

Assume data set G has a model \( y = 26(0.30)^x \) (from the options, this is a common form).

Step2: Transform for Data Set H

Data set H is created by multiplying G's \( y \)-values by 20? Wait, no—wait, the problem says "multiplying the \( y \)-value of each data point from data set G by 20"? Wait, no, re-reading: "data set H is created by multiplying the \( y \)-value of each data point from data set G by 20"? Wait, no, the options: let's check. Wait, maybe G's model is \( y = 26(0.30)^x \), and H is G's \( y \) times 20? No, wait, option c is \( y = 26(0.30)^x + 20 \)? No, wait, the problem says "multiplying the \( y \)-value... by 20"? Wait, no, maybe I misread. Wait, the options: a is \( y = 20(0.30)^x + 20 \), b is \( y = 26(0.30)^x \), c is \( y = 26(0.30)^x + 20 \), d is \( y = 522(0.30)^x \). Wait, no—wait, "multiplying the \( y \)-value of each data point from data set G by 20". So if G's model is \( y_G = 26(0.30)^x \), then H's model is \( y_H = 20 \times y_G = 20 \times 26(0.30)^x \)? Wait, no, 20×26=520, close to 522? Wait, maybe G's model is \( y = 26(0.30)^x \), and H is multiplying by 20, so \( y = 26 \times 20 \times (0.30)^x = 520(0.30)^x \), which is closest to option d: \( y = 522(0.30)^x \). Alternatively, maybe the original G model is \( y = 26(0.30)^x \), and H is multiplying by 20, so \( y = 26 \times 20 \times (0.30)^x = 520(0.30)^x \), which is approximately 522, so option d. Wait, but let's check the options again. Wait, the problem says "data set H is created by multiplying the \( y \)-value of each data point from data set G by 20". So if G's equation is, say, \( y = 26(0.30)^x \), then H's equation is \( y = 20 \times 26(0.30)^x = 520(0.30)^x \), which is closest to option d: \( y = 522(0.30)^x \). So the most appropriate model is d.

Answer:

d. \( y = 522(0.30)^x \)