Set 17: Exponential Functions

Explanation

Answer: A

An investment triples every 5 years. Which equation models the value after $t$ years if starting with $2,000?

$V(t) = 2000(3)^{t/5}$

✓ Correct

$V(t) = 2000(3)^{5t}$

$V(t) = 6000(t)$

$V(t) = 2000(3)^t$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Model the tripling pattern. 1. Growth Factor: Triples means multiply by 3. 2. Time Period: Every 5 years, so number of periods = $\frac{t}{5}$ . 3. Equation: $V(t) = 2000(3)^{t/5}$ . 4. Verify: At $t=5$ , $V = 2000(3)^1 = 6000$ (tripled) ✓ Strategic Tip: Exponent = $\frac{\text{elapsed time}}{\text{period length}}$ . Choice B is incorrect because $3^{5 t}$ grows much too fast. Choice C is incorrect because this is linear, not exponential. Choice D is incorrect because this triples every year, not every 5 years.

Key Steps:

•

The correct answer is $V(t) = 2000(3)^{t/5}$

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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Set 17: Exponential Functions

Detailed Explanation

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