PSAT Math Multiple-Choice Question 411: Answer and Explanation

Question: 411

Scientists are modeling population trends and have noticed that when a certain bacterial population changes, the change is based on a linear function of the amount of time elapsed in hours. When t = 21 hours, the population is 8 colonies, and when t = 35 hours, the population is 10 colonies. Which of the following best describes f (t)?

• A.
• B.
• C.
• D.

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Describing Real-Life Situations with Functions

Getting to the Answer: Because the slopes of all the answer choices are different, you can use the slope formula to determine which choice is correct. The number of colonies depends on the time elapsed, so start by writing the information given as ordered pairs in the form (time, number of colonies). Using the ordered pairs (21, 8) and (35, 10), the slope is .

The only choice with this slope is (C).