1. **State the problem:** We have three different models fitting the decay of a radioactive substance over time $x$ (in days) with amount $y$ (in milligrams). 2. **Identify the models:** - Figure 1: $y = 300(0.99)^x + 130$ - Figure 2: $y = 504(0.98)^x$ - Figure 3: $y = 0.03x^2 - 8x + 575$ 3. **Choosing the best fit:** Radioactive decay is typically modeled by an exponential decay function without an added constant or quadratic term. Figure 2's model $y = 504(0.98)^x$ is a pure exponential decay, which is most appropriate for radioactive decay. 4. **Predict the amount after 80 days using Figure 2's model:** $$y = 504(0.98)^{80}$$ Calculate the exponent: $$0.98^{80} = e^{80 \ln(0.98)}$$ Calculate $\ln(0.98) \approx -0.0202$: $$80 \times (-0.0202) = -1.616$$ So: $$0.98^{80} = e^{-1.616} \approx 0.198$$ Now multiply: $$y = 504 \times 0.198 = 99.79$$ 5. **Final answer:** After 80 days, the amount of radioactive substance is approximately **99.79 milligrams**. This matches the expected exponential decay behavior and fits the data best.