Schneider Pritchard
05/15/2023 · Junior High School
First, we find the initial amount in the sample. It occurs when 0 hours have passed. So, we let \( t=0 \) and compute \( A \) \[ A(0)=2400\left(\frac{1}{2}\right)^{\frac{0}{14}}=2400\left(\frac{1}{2}\right)^{0}=2400(1)=2400 \] The initial amount in the sample was 2400 grams. Next, we find the amount present after 30 hours. We let \( t=30 \) and use the calculator to compute \( A(30) \) \( A(30)=2400\left(\frac{1}{2}\right)^{\frac{30}{14}}=543.4 \ldots \) Rounding to the nearest gram, we get 543 grams.
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The initial amount in the sample is 2400 grams. After 30 hours, the amount is approximately 543 grams.
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