7. A radioactive isotope decays at a rate y'(t) = -ky(t) proportional to the amount y(t) remaining at time t. Express the half-life of the isotope in terms of the constant k. The half-life means the time it takes for y(t) to reach one half of its initial value y(0).

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7. A radioactive isotope decays at a rate
y'(t) = -ky(t)
proportional to the amount y(t) remaining at time t. Express the half-life of the isotope in
terms of the constant k. The half-life means the time it takes for y(t) to reach one half of
its initial value y(0).
Transcribed Image Text:7. A radioactive isotope decays at a rate y'(t) = -ky(t) proportional to the amount y(t) remaining at time t. Express the half-life of the isotope in terms of the constant k. The half-life means the time it takes for y(t) to reach one half of its initial value y(0).
Expert Solution
Step 1

Given:-

A radioactive isotope decays at a rate y'(t)=-ky(t) proportional to the amount y(t) remaining at time t.

To find:-

Express the half-life of the isotope in terms of the constant k.

Here 

The half-life means the time it takes for y(t) to reach one half of its initial value y(0).

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