# SAT Math Multiple Choice Question 674: Answer and Explanation

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**Question: 674**

**14.** A culture of bacteria initially contained *p* cells, where *p* > 100. After one hour, this population decreased by . In the second and third hours, however, the population increased by 40% and 50%, respectively. At the end of those first three hours, what was the population of the culture?

- A. 1.3
*p* - B. 1.4
*p* - C. 1.5
*p* - D. 1.6
*p*

**Correct Answer:** B

**Explanation:**

**B**

**Advanced Mathematics (exponential growth) MEDIUM**

We might begin by plugging in a number for *p*. Let's say *p* = 120 cells to start. We are told that after one hour the population decreased by . Since of 120 is 40, the population decreased by 40 and the population was then 120 - 40 = 80 cells. In the second hour, the population *increased* by 40%. Increasing a number by 40% is equivalent to it by 1.40 (because it becomes 140% of what it was), so the population was then 80(1.40) = 112 cells. In the third hour, the population *increased* by 50%, so it became 112(1.50) = 168 cells.

Substituting *p* = 120 into each of the answer choices yields (A) 1.3*p* = 1.3(120) = 156, (B) 1.4*p* = 1.4(120) = 168, (C) 1.5*p* = 1.5(120) = 180, and (D) 1.6*p* = 1.6(120) = 192. Therefore the answer is (B).

Alternately, you can solve this problem algebraically: *p*(2/3)(1.40)(1.50) = 1.40*p*.