Question

A radioactive substance decays exponentially. a scientist begins with 190 milligrams of a radioactive substance. after 17 hours, 95 mg of the substance remains. how many milligrams will remain after 21 hours

Answer 1

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