A radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 1

Question

A radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 prams right now. What will be the amount of the material right after 20 years?
a. 10 ln 2/ln(1000/980)
b. 10^6/980
c. 980^3/10^6
d. 980^2/10^3

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Jezebel 2 months 2021-07-24T15:14:27+00:00 1 Answers 4 views 0

Answers ( )

    0
    2021-07-24T15:15:39+00:00

    Answer:

    Amount left is 941.95 g.

    Step-by-step explanation:

    initial amount = 1000 g

    time = 10 years

    amount left =  980 grams

    Now

    980 = 1000 e^{-\lambda t}\\\\e^{\lambda\times 10}= 1.02\\\\10 \lambda  = ln 1.02\\\\\lambda  = 1.98\times10^{-3} per year

    time t = 20 years

    Let the amount is N.

    980 = 1000 e^{-\lambda t}\\\\e^{\lambda\times 10}= 1.02\\\\10 \lambda  = ln 1.02\\\\\lambda  = 1.98\times10^{-3} per year\\N = 980 e^{- 1.98\times 10^{-3}\times 20}\\\\ln N = ln 980 - 0.0396\\\\ln N = 6.88 - 0.0396 = 6.86\\\\N = 941.95 g

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