Losing the same percent each hour is exponential decay: the mass is multiplied by the same factor each hour, rather than reduced by a fixed number of grams. Subtract the percent lost from to find the percent remaining, then write it as a decimal multiplier. Raise that multiplier to the number of hours. The percent lost is not the amount you keep.
Hints
- Hint 1
A percent decrease takes part of the current mass away. Start with of the mass at the beginning of an hour. What percent remains after the given loss?
- Hint 2
The hourly multiplier is the decimal form of the percent remaining. What would you multiply the initial mass by to find the mass after one hour?
- Hint 3
In exponential decay, each hour's percent loss is taken from the updated mass. An exponent counts repeated multiplications. How many times has the hourly multiplier been applied after hours?
Step-by-step
Build the hourly decay model
Step 1Find the percent remaining
No Desmos needed. Finding the hourly percent remaining takes one subtraction; the rest is a repeated-percent rule.
The mass at the start of an hour is of that hour's mass. Since it loses each hour, subtract to find what's left:
- Step 2
Convert the percent to a multiplier
A multiplier is the number you multiply the current mass by to get the new mass. Convert the remaining to a decimal by dividing by :
Use the part remaining, not the part lost, as the multiplier.
- Step 3
Write the mass after one hour
The initial mass is . Multiply it by the hourly factor to write , the mass after one hour:
The loss is a fraction of the mass at that hour, not a fixed grams.
- Step 4
Repeat the factor for the number of hours
Each hour multiplies the updated mass by again. An exponent counts those repeated multiplications, so after hours:
This gives the mass remaining in grams. Choice C.