SAT Math Multiple Choice Question 397: Answer and Explanation

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Question: 397

7. A dendrologist (a botanist who studies trees exclusively) is examining the way in which a certain tree sheds its leaves. He tracks the number of leaves shed each day over the period of a month, starting when the first leaf is shed. He organizes the data in a scatterplot and sees that the data can be modeled using an exponential function. He determines the exponential model to be f(x) = 6(1.92)x, where x is the number of days after the tree began to shed its leaves. What does the value 1.92 in the function tell the dendrologist?

  • A. The number of leaves shed almost doubles each day.
  • B. The number of leaves shed almost doubles every six days.
  • C. The number of leaves left on the tree is reduced by about 92% each day.
  • D. The number of leaves left on the tree is reduced by about 92% every six days.

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Problem Solving and Data Analysis / Scatterplots

Strategic Advice: The dendrologist uses an exponential function to model the data. When an exponential equation is written in the form of f(x) = abx, a is the starting amount and b is the rate of growth or decay.

Getting to the Answer: Read the question carefully. The dendrologist is studying the number of leaves shed, not the number of leaves left on the tree, so you can eliminate C and D. Remember, a is the starting amount, not the unit of time, so it can't represent the number of days, which means you can also eliminate B. Choice (A) is correct because 1.92 is b in the equation, which represents the growth rate, so it tells the dendrologist that the number of leaves shed almost doubles (192% is very close to 200%) each day.

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