# 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.