# SAT Math Multiple Choice Question 240: Answer and Explanation

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**Question: 240**

**15.** A bacteria population, P, can be modeled by the equation P = P_{0}10^{kt}, where P_{0} is the bacteria population at the beginning of the experiment, t is the time in hours since the beginning of the experiment, and k is a positive constant. Which of the following gives the time, t, in terms of k, P, and P_{0} ?

- A.
- B.
- C.
- D.

**Correct Answer:** B

**Explanation:**

BWhenever there are variables in the question and in the answers, think Plugging In. If P_{0} = 4, k = 2, and t = 3, then P = (4)(10)^{6} = 4,000,000. Plug these values into the answer choices to see which answer works. Choice (A) becomes 3 = . Simplify the right side of the equation to get 3 = , then 3 = , and finally 3 = -3. This isn't true, so eliminate (A). Choice (B) becomes 3 = . Simplify the right side of the equation to get 3 = , then 3 = , and finally 3 = 3. Keep (B), but check the remaining answer choices just in case. Choice (C) becomes 3 = . Simplify the right side of the equation to get 3 = , or 3 ≈ 3.6. Eliminate (C). Choice (D) becomes 3 = 2log. Simplify the right side of the equation to get 3 = 2log, then 3 = 2(-6), and finally 3 = -12. Eliminate (D). The correct answer is (B).