The table shows the number of users of a new app at the end... | SAT Two-variable data: models and scatterplots Question, Answer Explained

Question bank / Two-variable data: models and scatterplots

Math · Problem-Solving and Data AnalysisEasy

Month	Number of users
1	2,000
2	3,000
3	4,500
4	6,750

The table shows the number of users of a new app at the end of each of its first $4$ months. Which of the following best describes the relationship between the month and the number of users?

Linear, because the number of users increases by the same amount each month

Linear, because the number of users increases by the same percentage each month

Exponential, because the number of users increases by the same amount each month

Exponential, because the number of users increases by the same percentage each month

Show answer and explanation

Answer: D

The increases are $1{,}000$ , $1{,}500$ , and $2{,}250$ , so the amount added each month isn't constant, and the relationship isn't linear. Each value is $1.5$ times the one before it, since $\frac{3{,}000}{2{,}000} = \frac{4{,}500}{3{,}000} = \frac{6{,}750}{4{,}500} = 1.5$ . Multiplying by the same factor each month means the users grow by the same percentage, $50\%$ , which is exponential growth.

Choice A is tempting because the first increase is a round $1{,}000$ , but the later increases are $1{,}500$ and $2{,}250$ .

Why the other choices are wrong

A. The increases are 1,000, then 1,500, then 2,250, so the amount added each month is not constant.
B. Growth by the same percentage each month is exponential, not linear.
C. The amounts added each month are different; it is the growth factor, 1.5, that stays the same.

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