Subjects algebra

Exponential Decay 6F8Df6

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1. The problem asks to predict the amount after 50 days using the best fitting curve, which is given as Figure 3: $$y = 546(0.98)^x$$. 2. The formula for exponential decay is $$y = a b^x$$ where $$a$$ is the initial amount and $$b$$ is the decay factor (between 0 and 1). 3. To find the amount after 50 days, substitute $$x = 50$$ into the equation: $$y = 546(0.98)^{50}$$ 4. Calculate $$0.98^{50}$$: $$0.98^{50} \approx 0.3641696801$$ 5. Multiply by 546: $$y \approx 546 \times 0.3641696801 = 198.27$$ 6. Therefore, the predicted amount after 50 days is approximately **198.27 milligrams**.