Set 11: Exponential Functions (Advanced)

Explanation

Answer: C

In the function $V(t) = 2500(1.08)^t$ , which describes the value of an investment over time, what does the number 1.08 represent?

The initial investment was $1.08.

The investment grows by $1.08 each year.

The investment grows by 8% each year.

✓ Correct

The investment grows by 108% each year.

Detailed Explanation

Choice C is correct. Choice C is the correct answer. The base 1. $08$ indicates the percentage growth rate. 1. Analyze Base: The growth factor is $b = 1.08$ . 2. Find Rate: Since $b = 1 + r$ , we have $1.08= 1 + r$ , so $r = 0.08$ . 3. Convert to %: $0.08= 8\%$ . Strategic Tip: To find the percentage rate from the factor $1.XX$ , just look at the decimal part $XX$ . Choice A is incorrect because the initial investment is 2500. Choice B is incorrect because exponential growth is by a percentage, not a fixed dollar amount. Choice D is incorrect because 108% growth would mean $b = 2.08$ .

Key Steps:

•

The correct answer is The investment grows by 8% each year.

Why others are wrong:

A: Choice A is incorrect and may result from a calculation error.

B: Choice B 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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Set 11: Exponential Functions (Advanced)

Detailed Explanation

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