Set 2: Exponential Functions (Intermediate)

Explanation

Answer: C

A car purchased for $20,000 depreciates at a rate of 15% per year. Which equation models its value $V(t)$ ?

$V(t) = 20000(0.15)^t$

$V(t) = 20000(1.15)^t$

$V(t) = 20000(0.85)^t$

✓ Correct

$V(t) = 20000 - 15t$

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Depreciation means decay. 1. Identify Rate: $r = 15\% = 0.15$ . 2. Calculate Factor: $b = 1 - r = 1 - 0.15 = 0.85$ . 3. Form Equation: $V(t) = 20000(0.85)^t$ . Strategic Tip: For depreciation, the base must be less than 1. Choice A is incorrect because 0.15 would mean losing 85% per year. Choice B is incorrect because 1.15 means the car gains value. Choice D is incorrect because it represents linear depreciation.

Key Steps:

•

The correct answer is $V(t) = 20000(0.85)^t$

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.

← Previous Next →

🎯 Keep Practicing!

Master all sections for your best SAT score

📚Reading & Writing→📖Vocabulary→