Question

It is known that the mass, m(t), of a radio-active substance decreases as it decays, and that the equation governing this is m′(????)=−0.015m(????) where t is in years. What is the half-life? (Hint: Find an exponential function which solves the equation. You will then have a formula for the mass, so you can find the half-life.)

Answer 1

46.2 years

Explanation:

You recognize that the solution to the differential equation will be ...

m(t) = c·e^(-0.015t) . . . . . . .for some c dependent upon initial conditions

and that the half-life will be the answer to ...

ln(1/2) = -0.015t . . . . . . . . . use c=1, m=1/2, and take the natural log

t = ln(1/2)/-0.015 ≈ 46.2

The half-life will be about 46.2 years.