SAT Math Multiple Choice Question 637: Answer and Explanation

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Question: 637

7. During a coyote repopulation study, researchers determine that the equation P = 250(1.32)t describes the population P of coyotes t years after their introduction into a new region. Which of the following gives the values of I, the initial population of coyotes, and r, the annual percent increase in this population?

  • A. I = 250, r = 32%
  • B. I = 250, r = 132%
  • C. I = 330, r = 32%
  • D. I = 330, r = 132%

Correct Answer: A

Explanation:

A

Advanced Mathematics (parabolas) MEDIUM

The initial population, I, is the population when the time is 0. Therefore, I = 250(1.32)0 = 250(1) = 250. The annual percent increase in the population, r, can be calculated by finding the population at t = 1 and then calculating the percent change from the initial population. If t = 1, P = 250(1.32)1. As we discussed in Chapter 8, Lesson 7, multiplying a quantity by 1.32 is equivalent to increasing a number by 32% (that is, 1.32 = 100% + 32%), so r = 32%.

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