4
advanced-math

The value of a rare trading card is modeled by V(t)=100(2)tV(t) = 100(2)^t, where tt is the number of years since purchase. What is the value of the card after 3 years?

A

$200

B

$600

C

$800

D

$1000

Correct Answer: C

Choice C is the correct answer. Substitute t=3t=3 into the equation.

  1. Substitute: Replace tt with 3 in the function: V(3)=100(2)3V(3) = 100(2)^3.
  2. Exponentiate: Calculate 23=2×2×2=82^3 = 2 \times 2 \times 2 = 8.
  3. Multiply: 100×8=800100 \times 8 = 800.

💡 Strategic Tip: Follow the order of operations (PEMDAS). Exponents first, then multiplication.

Choice A is incorrect because it calculates 100×2100 \times 2 first (linear thinking). Choice B is incorrect because it calculates 100×2×3100 \times 2 \times 3 (linear growth). Choice D is incorrect because it miscalculates 232^3 as 10 or adds.