Question

The radioactive substance strontium-90 has a half-life of 28 years. In other words, it takes 28 years for half of a given quantity of strontium-90 to decay to a non-radioactive substance. The amount of radioactive strontium-90 still present after t years is modeled by the expression 80x2^-t/28 grams. Evaluate the expression for t = 0, t = 28 and t = 56. What does each value of the expression represent?

Answer 1

\[N(t)=N_02^{-t/t_{1/2}}\]

Answer 2

\[t_{1/2}=28\text{ years}\]

Answer 3

\[N_0=80\text{ grams}\]

Answer 4

\[N(t) \text{ grams}=80\cdot2^{-t/28 yr}\text{ grams}\]

Answer 5

\[N(0) \text{ g}=80\cdot2^{-0\text{ yr}/28\text{ yr}}\text{ g}\]\[\qquad\qquad=80\cdot2^0\text g\]\[\qquad\qquad=80\text { g}\]
\[N(28 \text { yr}) \text{ g}=80\cdot2^{-28\text { yr}/28 \text{ yr}}\text{ g}\]\[\qquad\qquad=\cdots\]
\[N(56 \text { yr}) \text{ g}=80\cdot2^{-56\text { yr}/28 \text{ yr}}\text{ g}\]\[\qquad\qquad=\cdots\]