Problem

A sample of 550 grams of radioactive substance decays according to the function $A(t)=550 e^{-.035 t}$, where $t$ is the time in years. How much of the substance will be left in the sample after 20 years? Round your answer to the nearest whole gram.
A. 167 grams
B. 273 grams
C. 0 grams
D. $1 \mathrm{gram}$

Answer

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Answer

Final Answer: The amount of the substance left in the sample after 20 years is \(\boxed{273}\) grams.

Steps

Step 1 :Given a sample of 550 grams of radioactive substance that decays according to the function \(A(t)=550 e^{-0.035 t}\), where \(t\) is the time in years.

Step 2 :We are asked to find how much of the substance will be left in the sample after 20 years. This can be found by substituting \(t=20\) into the function \(A(t)=550 e^{-0.035 t}\) and calculating the result.

Step 3 :Substitute \(t=20\) into the function to get \(A(20)=550 e^{-0.035 \times 20}\).

Step 4 :Calculate the result to get \(A(20) = 273\) grams.

Step 5 :Final Answer: The amount of the substance left in the sample after 20 years is \(\boxed{273}\) grams.

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