Digital SATMath: AlgebraMedium
A financial analyst is modeling the depreciation of a company's asset. The value of the asset, V, in dollars, after t years is given by the function V(t) = 50000(0.85)^t. What is the annual rate of depreciation?
- A15%
- B85%
- C50%
- D150%
Show answer & explanationAnswer & explanation
Correct answer: A. 15%
The general form for exponential decay is A(t) = P(1 - r)^t, where r is the decay rate. Comparing this to the given function V(t) = 50000(0.85)^t, we have 1 - r = 0.85. Solving for r gives r = 1 - 0.85 = 0.15, which is 15%.
Why the other options are wrong
- B. This is the decay factor itself, not the rate of depreciation.
- C. This is an incorrect interpretation of the decay factor.
- D. This is an incorrect calculation and understanding of depreciation.
Exponential Decay Rate
The rate at which a quantity decreases over time in an exponential decay model.
- Represented by 'r' in the formula A(t) = P(1 - r)^t.
- It is derived from the decay factor (1-r).
- Expressed as a decimal or percentage.
Memory trick: Decay models decrease, so look for a factor less than one!