The function f(t) = 60,000(2)t/410 gives the number of bacteria in a population t minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?
Correct answer: A. 410
- A. 410
- B. 310
- C. 210
- D. 420
Explanation
The correct answer is 410. The exponential function f(t) = 60,000(2)t/410 represents the growth of the bacteria population over time. The doubling time is determined by how long it takes for the exponent in the expression 2t/410 to increase by 1. Since the exponent is t/410, it requires an increase of 410 in t for the exponent to become 1, causing the population to double. Option B (310) and Option C (210) underestimate this required increase, while Option D (420) overestimates it.
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