The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = -.022m, where m is the mass of the isotope in mg and t is the time in years.

Question

A. If m(0)=20, write a function m(t) for the radioactive decay of the isotope. Show the steps in separating variables of the given differential equation and solving the equation for m.

B. The half-life of a radioactive substance is the time required for half of the substance to decay. What is the half-life of this radioactive isotope to the nearest tenth of a year?

Answer 1

c'mon, you can do this.

dm/dt = -0.22m
dm/m = -0.22 dt
ln(m) = -0.22t + c
m = c e^(-0.22t)

c is the initial amount, so

m(t) = 20 e^(-0.22t)

I'm sure you can find the half-life now, ok?

Answer 2

Steve ur a savage

Answer 3

Thank you

Answer 4

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