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Harman [31]
3 years ago
9

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

e 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
Mathematics
1 answer:
Mandarinka [93]3 years ago
7 0

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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