Math  /  Calculus

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A sample of 9 grams of radioactive material is placed in a vault. Let P(t)P(t) be the amount remaining after tt years, and let P(t)P(t) satisfy the differential equation P(t)=0.032P(t)P^{\prime}(t)=-0.032 P(t). Answer parts (a) through (g)(\mathrm{g}). B. Solve 0.119=0.032P(t)-0.119=-0.032 P(t) for P(t)P(t). C. Evaluate P(t)=0.032(0.119)P^{\prime}(t)=-0.032(-0.119). D. Evaluate P(t)=0.032P(0.119)P^{\prime}(t)=-0.032 P(-0.119).
There will be \square of radioactive material left when it is disintegrating at a rate of 0.119 gram per year. (Type an integer or decimal rounded to one decimal place as needed.)

Studdy Solution
There will be approximately **3.7** grams of radioactive material left when it is disintegrating at a rate of 0.119 gram per year.

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