Math  /  Calculus

QuestionA 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)(a) through (g)(g). (e) How fast is the sample disintegrating when just 1 gram remains? Use the differential equation.
Choose the correct process to find how fast the sample disintegrating when just 1 gram remains. A. Evaluate P(t)=0.032(1)P^{\prime}(t)=-0.032(1). B. Solve 1=0.032P(t)1=-0.032 P(t) for P(t)P(t). C. Evaluate P(t)=0.032P(1)P^{\prime}(t)=-0.032 P(1). D. Solve P(1)=0.032P(t)P^{\prime}(1)=-0.032 P(t) for P(t)P(t).

Studdy Solution
The sample is disintegrating at a rate of 0.032-0.032 grams per year when just 1 gram remains.
This corresponds to answer choice A.

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