7

Set 12: Exponential Functions (Advanced)

Explanation

Answer: A

If y=5(1.06)ty = 5(1.06)^t, what is the percentage rate of change?

A.

Increase of 6%

✓ Correct
B.

Increase of 106%

C.

Decrease of 6%

D.

Increase of 0.06%

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Extract the rate from the growth factor. 1. Identify Factor: b=1.06b = 1.06. 2. Compare to 1: 1.06=1+0.061.06= 1 + 0.06. 3. Convert: 0.06=6%0.06= 6\%. Strategic Tip: The decimal part after the 1 is your percentage growth. Choice B is incorrect because 106% growth would mean b=2.06b=2.06. Choice C is incorrect because b>1b > 1 implies growth, not decay. Choice D is incorrect because 0.06% would be b=1.0006b=1.0006.

Key Steps:

The correct answer is Increase of 6%

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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