A radioactive substance decays at a rate such that its mass is reduced to 75% of its original amount every 3 years. If the initial mass is 800 grams, the mass after 9 years will be _______ grams.
Answer & Analysis
Analysis
Question Analysis
This question assesses the student's understanding of exponential decay in a real-world context. The key is to identify the initial mass, the decay factor, and the time period.
Key Concept Explanation
Exponential decay is characterized by a quantity that decreases by a fixed percentage over equal intervals of time. The general form of the exponential function is (), where is the initial quantity, is the decay factor, and is the number of time periods.
Step-by-step Solution
1. Identify the initial mass: grams.
2. Determine the decay factor: Since the mass is reduced to 75% every 3 years,
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