To find the amount of Radium-226 remaining after 7 years using the equation \( A(t) = 450e^{-0.0004t} \), we substitute \( t = 7 \) into the equation.
\[ A(7) = 450e^{-0.0004 \times 7} \]
First, we calculate \( -0.0004 \times 7 \):
\[ -0.0004 \times 7 = -0.0028 \]
Next, we compute the value of \( e^{-0.0028} \):
\[ e^{-0.0028} \approx 0.9972 \quad (\text{using a calculator or exponent table}) \]
Now substituting this value back into the equation:
\[ A(7) = 450 \times 0.9972 \]
Calculating this gives:
\[ A(7) \approx 448.74 \]
Rounding to the nearest tenth, we find:
\[ A(7) \approx 448.7 \]
Thus, after 7 years, approximately 448.7 grams of Radium-226 will remain.
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