Value Depreciation

3
advanced-math

Which function represents a quantity that starts at 500 and decreases by 20% each year?

A

y=500(0.20)ty = 500(0.20)^t

B

y=500(1.20)ty = 500(1.20)^t

C

y=500(0.80)ty = 500(0.80)^t

D

y=20(500)ty = 20(500)^t

Correct Answer: C

Choice C is the correct answer. Convert percentage decrease to a decay factor.

  1. Identify Rate: Decrease of 20% means r=0.20r = 0.20.
  2. Calculate Factor: b=1r=10.20=0.80b = 1 - r = 1 - 0.20 = 0.80.
  3. Form Equation: y=500(0.80)ty = 500(0.80)^t.

💡 Strategic Tip: If you lose 20%, you keep 80%. The factor is what you keep.

Choice A is incorrect because 0.20 would mean losing 80% per year. Choice B is incorrect because 1.20 represents a 20% increase. Choice D is incorrect because it has the wrong structure entirely.