To solve this item, we need write first all the necessary data to solve the problem. Governing principle of this problem is basically exponential decay of a certain substance.
Given:
Let t represents time
N represents mass of substance
Initially,
at t(0), N(0) = 190mg radioactive substance
at t(17), N(17) = 95mg radioactive substance
Required: N(21)
Solution:
We write first the formula for exponential decay, that is
N(t) = N(0)*e^(-k*t) ; k = exponential decay constant
We need first to determine the k, substituting the given we have
95 = 190*e^(-k*17)
Dividing by 190, we get
0.5 = e^(-k*17)
To eliminate the exponential e, we take the natural logs of both sides
ln(0.5) = ln(e^(-k*17))
-0.693 = -k*17
Solving for k,
k = 0.04077
To solve for N(21), we need to substitute k to the original equation
N(21) = N(0)e^(-k*21)
N(21) = 190*e^(-0.04077*21)
N(21) = 80.7 mg
ANSWER: 80.7 mg radioactive substance left after 21 hours
