SAT Math Multiple Choice Question 768: Answer and Explanation

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Question: 768

3. P(t) = 250(2.4)t

The formula above shows the relationship between the population, P, of a certain mushroom species on a one-acre plot of land as a function of t, the number of weeks that have passed since the mushrooms were first introduced on the plot.

What is the meaning of the number 250 in the formula above?

  • A. The plot initially contained 250 mushrooms.
  • B. The population of mushrooms increases by 250 mushrooms per week.
  • C. The population of mushrooms increases by 250% each week.
  • D. It will take 250 weeks for the population of mushrooms to double.

Correct Answer: A

Explanation:

A

Advanced Mathematics (exponential functions) MEDIUM

Notice that substituting t = 0 into the function gives us P(0) = 250(2.4)0 = 250(1) = 250. Therefore, the number 250 in the equation means the population of mushrooms on the plot when t = 0.

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