SAT Two-variable data: models and scatterplots Practice Question 3 (Medium)

Question bank / Two-variable data: models and scatterplots

Math · Problem-Solving and Data AnalysisMedium

$x$	0	1	2	3
$y$	5	7.5	11.25	16.875

The table shows values of $x$ and $y$ for a relationship. Which of the following equations best models the relationship?

$y = 2.5x + 5$

$y = 5x + 1.5$

$y = 1.5(5)^x$

$y = 5(1.5)^x$

Show answer and explanation

Answer: D

The differences between consecutive $y$ -values are $2.5$ , $3.75$ , and $5.625$ , so the relationship isn't linear. The ratios are constant: $\frac{7.5}{5} = \frac{11.25}{7.5} = \frac{16.875}{11.25} = 1.5$ . An exponential model with initial value $5$ (at $x = 0$ ) and growth factor $1.5$ is $y = 5(1.5)^x$ .

Choice A fits the first two points but not the rest, because the increases are not constant.

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