In an exponential decay model, a factor below repeatedly multiplies the current amount. Read the time interval from the denominator in the exponent, then compare the factor with to find the percent lost. Each percent loss comes from the updated value, not the original value. A fixed dollar loss would describe a different pattern.
Hints
- Hint 1
The exponent counts how many times the factor has been applied. Since is in years, how long does it take for to increase by ? That's the time between multiplications.
- Hint 2
A multiplier of means remains after one interval. Start with the whole and subtract what's left. What percent of the value at the start of that interval was lost?
Step-by-step
Read the interval and multiplier
Step 1Find when the factor acts
No Desmos needed. The exponent and base give the interval and percent directly.
The exponent counts uses of the factor. Because is measured in years, reaches after half a year. So the factor acts once every year, or months.
- Step 2
Find the percent lost
The multiplier keeps of the value at the start of each interval. To find the percent lost, subtract the part kept from the whole:
- Step 3
Interpret the repeated decrease
The factor multiplies the updated value each time, so the dollar amount lost isn't fixed. Every months, the machine's value decreases by of its value at the start of that six-month interval. Choice C.