A radioactive substance decays exponentially. A scientist begins with 190 milligrams of a radioactive substance. After 33 hours, 95 mg of the substance remains. How many milligrams will remain after 51 hours? mg Give your answer accurate to at least one decimal place. Submit Question Jump to Answer

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Question:

A radioactive substance decays exponentially. A scientist begins with 190 milligrams of a radioactive
substance. After 33 hours, 95 mg of the substance remains.
How many milligrams will remain after 51 hours?
mg
Give your answer accurate to at least one decimal place.
Submit Question
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Answer: 65.1 (mg)Step-by-step explanation:[tex]y=190*e^{-a*t}\\\\Calculate\ a:\\\\t=33,y=95(mg)\\\\190*e^{-a*33}=95\\\\e^{-a*33}=0.5\\\\-a*33=ln(0.5)\\\\a=\dfrac{ln(\dfrac{1}{2}) }{-33} \\\\a=0,02100... \approx{0.021}\\\\If\ t=51\ h, y=190*e^{-0.02100*51}=65.09167...\approx{65.1}[/tex]

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