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A sample of 400 grams of radioactive substance decays according to the function A(t) = 400e^-.046t, 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.

Respuesta :

Answer: There will be 0.04 grams will be left in the sample after 20 years.

Step-by-step explanation:

Since we have given that

[tex]A(t)=400e^{-0.46t}[/tex]

Here, Initial amount of radioactive substance = 400 grams

We need to find the amount of substance that will be left in the sample after 20 years.

So, t = 20 years

So, it becomes,

[tex]A(t)=400e^{-0.46\times 20}\\\\A(t)=400e^{-9.2}\\\\A(t)=0.04\ grams[/tex]

Hence, there will be 0.04 grams will be left in the sample after 20 years.

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