Exponential decay describes a process where a quantity decreases over time at a rate proportional to its current value. Think of it like the value of a car depreciating each year, or a radioactive substance losing its mass. The key is that the amount of decrease is larger at the beginning and slows down as time goes on. The general formula for exponential decay is $y = a(1 - r)^t$, where $y$ is the final amount, $a$ is the initial amount, $r$ is the rate of decay (expressed as a decimal), and $t$ is time.
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Decay Factor | A. The initial amount before decay. |
| 2. Initial Value | B. The time elapsed during decay. |
| 3. Decay Rate | C. The base (1 - r) in the exponential decay equation. |
| 4. Time Period | D. The percentage decrease expressed as a decimal. |
| 5. Final Value | E. The amount remaining after decay. |
Complete the following paragraph using the words: exponential, decreases, rate, time, initial.
__________ decay occurs when a quantity __________ over __________ at a constant __________. The equation uses the __________ value to find the decayed value.
Explain, in your own words, how the decay rate affects the final value in an exponential decay problem. Give an example to support your explanation.
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