PSAT Math Multiple-Choice Question 430: Answer and Explanation

Question: 430

A scientist is studying the average annual growth of trees in a newly planted forest. The average height of the trees was 3.6 feet when they were planted, and they have grown an average of 2.4 feet per year since then. The scientist has been studying the growth of the trees for five years. If she uses the function g(y) = h + 2.4(y), where h is the height (in feet) of the trees five years after they were planted and y is the number of years after the fifth year, to determine the expected further growth of these trees from the sixth year onward, which of the following would be included in the range of the scientist's results?

• A. 6
• B. 10.8
• C. 15.4
• D. 18

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Describing Real-Life Situations with Functions

Getting to the Answer: The range of the function is all of the possible g(y) values. So this question asks you to determine which numbers are too small to be part of the range of the scientist's data.

First, calculate how tall the trees would be when the scientist begins to use her function: h = 3.6 + 2.4(5) = 15.6 feet. Having solved for h, the function can now be written as g(y) = 15.6 + 2.4y, where y is greater than or equal to 0, and the range will be any value greater than or equal to 15.6. Only (D) is larger than 15.6, so it is correct.