Exponential decay refers to a process where a quantity decreases at a rate proportional to its current value. Based on your options, here are the correct examples of exponential decay:
A. A vehicle depreciates 13% each year. - This is an example of exponential decay.
D. Air pressure decreases 12% for every 1000 meters in height. - This can be modeled as exponential decay and is a valid example.
G. A radioactive element has a decay rate of 10%. - This is another classic example of exponential decay.
The other options either describe growth or do not represent exponential decay:
- B. A tree is doubling in height each year. (This is exponential growth.)
- C. An investment earns a 5% interest each year. (This is also a form of exponential growth if compounded.)
- E. The population of a town is growing at an annual rate of 3.5%. (This is exponential growth.)
- F. A retirement account decreases by $12,000 each year. (This is a linear decrease, not exponential decay.)
So, the correct answers are A, D, and G.