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Advanced Math / Nonlinear functions Difficulty: Medium

The graph gives the estimated population $y$ , in thousands, of a town $x$ years since $2003$ , where $0 \leq x \leq 5$ . Which of the following best describes the increase in the estimated population from $x equals 0$ to $x equals 1$ ?

The estimated population at $x equals 1$ is $0.5$ times the estimated population at $x equals 0$ .

The estimated population at $x equals 1$ is $1.5$ times the estimated population at $x equals 0$ .

The estimated population at $x equals 1$ is $2.5$ times the estimated population at $x equals 0$ .

The estimated population at $x equals 1$ is $3.5$ times the estimated population at $x equals 0$ .

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Explanation

Choice B is correct. On the graph shown, the y-axis represents estimated population, in thousands. The graph shows that when $x equals 0$ , the y-coordinate is $6$ . Therefore, the estimated population at $x equals 0$ is $6$ thousand. The graph also shows that when $x equals 1$ , the y-coordinate is $9$ . Therefore, the estimated population at $x equals 1$ is $9$ thousand. Dividing $9$ thousand by $6$ thousand yields $1.5$ ; therefore, $9$ thousand is $1.5$ times $6$ thousand. It follows that the estimated population at $x equals 1$ is $1.5$ times the estimated population at $x equals 0$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.