Calculus

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.

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?

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  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?

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  2. Steve ur a savage

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