An exponential decay model repeatedly multiplies a quantity by a factor below . In a form like , the exponent counts -unit intervals, so read it before interpreting the factor. The factor tells what remains each interval, not what is lost. Don’t assume the factor applies every day.
Hints
- Hint 1
The exponent counts how many times the factor has been applied. If the exponent is , how many days must pass for it to increase by ?
- Hint 2
A decay factor below gives the fraction left after one interval. The fraction lost is the rest of the whole. Which of those does the factor itself describe?
Step-by-step
Read the interval, then the factor
Step 1Find when the factor applies
No Desmos needed. The exponent and factor give the interpretation directly. In the exponent , counts days. Every -day increase in adds to the exponent, so is applied every days, not every day.
- Step 2
Interpret what the factor keeps
A factor multiplies the previous mass to give the mass after one interval. Since , of the previous mass remains every days. The factor describes what’s left, not what’s lost. Choice C.