\( t = 9 \, \text{سنوات} \) (الوقت المنقضي)،
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- إذا كان لمادة مشعة عمر نصف يبلغ 3 سنوات، فما مقدار عينة وزنها 160 جرامًا المتبقية بعد 9 سنوات؟
- \[ \text{الكمية المتبقية} = P \times \left(\frac{1}{2}\right)^{t/T} \]
- \( P = 160 \, \text{جرام} \)،
- \( T = 3 \, \text{سنوات} \) (عمر النصف).
- \[ \text{الكمية المتبقية} = 160 \times \left(\frac{1}{2}\right)^{9/3} = 160 \times \left(\frac{1}{2}\right)^3 = 160 \times \frac{1}{8} = 20 \, \text{جرام} \]
- حل المعادلة التربيعية \( 3x^2 - 12x + 9 = 0 \).
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