Question

A radioactive material decays according to the formula A=A010^-kt where A is the final amount, A0 is the initial amount, and t is the time in years. Find k, if 500 grams of this material decays to 450 grams in 10 years. [Round the answer to 4 decimal places.]

A) 0.0046
B) 1.1065
C) -16.9897
D) -0.9000

Answer 1

500(10)^(-10k) = 450
10^(-10k) = 9/10
take log of both sides
-10k log10 = log (9/10) , but log 10 = 1
-10k = -.04576
k = .004576

Answer 2

A radioactive decay of an unknown substance is given by A(t)=Aoe^-kt where A(t) is the amount of substance (in grams) remaining at anytime (t) in hours. So is the initial amount of the substance before it started decaying and k is a proportionality constant.(Leave your answer correct to 2 decimal places).
a) If after two hours, 0.9 Ao remains, find k