A repeated percent decrease signals exponential decay: the amount is multiplied by the same fraction after each fixed stretch of time. Start with the original amount, use the fraction remaining as the multiplier, and divide elapsed time by the interval length to count repetitions. Using the percent lost as the multiplier models what disappears, not what remains.
Hints
- Hint 1
A percent decrease tells you what is removed, but the model needs the part left. Start with the whole mass, or , and subtract the percent lost. What fraction remains after one decrease?
- Hint 2
In an exponential model, the exponent counts how many times the multiplier applies, not how many years pass. If one decrease happens every 8 years, how many decreases have happened after years?
Step-by-step
Build the model from start, factor, and interval
Step 1Identify the starting mass
No Desmos needed. You're building a model from the words, not evaluating a given formula. The sample starts at 180 grams, so is the initial value, the number in front of the power.
- Step 2
Find the multiplier for one decrease
Each decrease removes of the mass present then. Subtract that from the whole to find the decay factor, the number that multiplies the mass each time: . The is lost; isn't the fraction remaining.
- Step 3
Count the 8-year intervals
The exponent counts applications of the multiplier. Since one decrease happens every 8 years, years contains intervals. At , , so the factor applies once. Using would apply it times by year .
- Step 4
Write the mass model
Put the starting mass, factor, and interval count together: . The base is what remains each interval; the exponent counts the intervals. So this equation gives the mass remaining, in grams, after years. Choice D.