Question

Question
Which of the following are examples of exponential decay? Select all that apply.
Responses

A vehicle depreciates 13%
each year.
A vehicle depreciates 13 percent each year.

A tree is doubling in height each year.
A tree is doubling in height each year.

An investment earns a 5%
interest each year.
An investment earns a 5 percent interest each year.

Air pressure decreases 12%
for every 1000
meters in height.
Air pressure decreases 12 percent for every 1000 meters in height.

The population of a town is growing at an annual rate of 3.5%
.
The population of a town is growing at an annual rate of 3 point 5 percent.

A retirement account decreases by $12,000
each year.
A retirement account decreases by 12 dollars comma 000 each year.

A radioactive element has a decay rate of 10%
.
A radioactive element has a decay rate of 10 percent.

Answer 1

Exponential decay refers to a process where a quantity decreases at a rate proportional to its current value. Based on this definition, the following responses are examples of exponential decay:

1. **A vehicle depreciates 13% each year.**
2. **Air pressure decreases 12% for every 1000 meters in height.**
3. **A retirement account decreases by $12,000 each year.** (Note: This is technically linear decay, but if it were related to a percentage of the account balance each year, it would be exponential decay.)
4. **A radioactive element has a decay rate of 10%.**

The responses that do **not** represent exponential decay are:

1. **A tree is doubling in height each year.** (This is exponential growth.)
2. **An investment earns a 5% interest each year.** (This is also exponential growth.)
3. **The population of a town is growing at an annual rate of 3.5%.** (This is again exponential growth.)

So, the correctly identified examples of exponential decay are:

- A vehicle depreciates 13% each year.
- Air pressure decreases 12% for every 1000 meters in height.
- A radioactive element has a decay rate of 10%.