7

Set 14: Exponential Functions (Intermediate)

Explanation

Answer: A

The population of bacteria in a petri dish is recorded:

HourCount
0100
3800
66,400

What is the growth factor per 3-hour period?

A.

8

✓ Correct
B.

2

C.

64

D.

700

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Calculate the ratio per time period. 1. Period 1: 800100=8\frac{800}{100} = 8. 2. Period 2: 6400800=8\frac{6400}{800} = 8. 3. Growth Factor: Every 3 hours, the count multiplies by 8. Strategic Tip: Growth factor = new valueold value\frac{\text{new value}}{\text{old value}} over one time period. Choice B is incorrect because this would only give 100 → 200 → 400. Choice C is incorrect because this is (6400100)(\frac{6400}{100}), not per period. Choice D is incorrect because this is the difference, not the ratio.

Key Steps:

The correct answer is 8

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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