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advanced-math

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

A

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

B

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

C

V(t)=6000(t)V(t) = 6000(t)

D

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

Correct Answer: A

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 = t5\frac{t}{5}.
  3. Equation: V(t)=2000(3)t/5V(t) = 2000(3)^{t/5}.
  4. Verify: At t=5t=5, V=2000(3)1=6000V = 2000(3)^1 = 6000 (tripled) ✓

💡 Strategic Tip: Exponent = elapsed timeperiod length\frac{\text{elapsed time}}{\text{period length}}.

Choice B is incorrect because35t3^{5t} 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.