einsteinium - 253 is an element that loses about $\frac{2}{3}$ of its mass every month. a sample of…
einsteinium - 253 is an element that loses about $\frac{2}{3}$ of its mass every month. a sample of einsteinium - 253 has 450 grams. write a function that gives the samples mass in grams, $s(t)$, $t$ months from today. $s(t)=$
Answer
Explanation:
Step1: Identify decay - type
The element loses $\frac{2}{3}$ of its mass each month, so the remaining fraction of mass each month is $1-\frac{2}{3}=\frac{1}{3}$. This is an exponential - decay problem.
Step2: Write the general form of exponential - decay function
The general form of an exponential function is $S(t)=S_0\cdot r^t$, where $S_0$ is the initial amount, $r$ is the decay factor, and $t$ is the time. Here, $S_0 = 450$ grams (the initial mass of the sample) and $r=\frac{1}{3}$ (the fraction of mass remaining each month).
Step3: Substitute values into the function
Substitute $S_0 = 450$ and $r=\frac{1}{3}$ into the formula $S(t)=S_0\cdot r^t$. We get $S(t)=450\cdot(\frac{1}{3})^t$.
Answer:
$S(t)=450\cdot(\frac{1}{3})^t$