Exponential decay is the process by which an amount decreases by a consistent percentage over equal time intervals. To determine which of the given contexts represents exponential decay, we must look for a situation in which the value decreases by a constant percentage over time.
Let's analyze each scenario:
1. A car depreciates at a rate of 2.2% per year.
This scenario describes a situation where the value of the car decreases by 2.2% each year. This is a classic example of exponential decay, as the amount of depreciation is a fixed percentage of the remaining value of the car each year.
2. A town's population grows at a rate of 8.9% every year.
This represents exponential growth, not decay, as the population is increasing by 8.9% each year.
3. An elevator descends at a rate of 21 feet per second.
This is a linear rate of decline, not exponential. The elevator is descending at a constant speed, not at a rate that changes as it descends.
4. A certain population of aggressive zombies quintuples every month.
This scenario is an example of exponential growth since the population size is increasing fivefold every month, not decreasing.
Therefore, the context that represents exponential decay is the first scenario, where a car depreciates at a rate of 2.2% per year.
