An unstable radioactive isotope decays according to the equation $y=2.53(.97)^{t}$ where $y$ is the number of grams remaining and $t$ is the time measured in minutes. Match each question with one of the solutions A, B, C, or D.
-How long will it take for the material to decay to half its initial amount?
A) Evaluate $2.53(.97)^{1 / 2}$
B) Evaluate $2.53(.97)^{2}$
C) Solve $2=2.53(.97)^{t}$
D) Solve $\frac{1}{2}(2.53)=2.53(.97)^{t}$

Question

Quizplus · Accepted Answer

To find the time it takes for the material to decay to half its initial amount, you need to solve for $t$ when the amount of material left, $y$, is half of the initial amount, which is $2.53$ grams. Therefore, you set $y$ to $\frac{1}{2}(2.53)$ and solve for $t$, which corresponds to option D.

An Unstable Radioactive Isotope Decays According to the Equation y=2.53(.97)ty=2.53(.97)^{t}y=2.53(.97)t Where yyy

An Unstable Radioactive Isotope Decays According to the Equation $y=2.53(.97)^{t}$ Where $y$