in a lab experiment, the decay of a radioactive isotope is being observed. at the beginning of the first day…
in a lab experiment, the decay of a radioactive isotope is being observed. at the beginning of the first day of the experiment the mass of the substance was 1300 grams and mass was decreasing by 14% per day. determine the mass of the radioactive sample at the beginning of the 11th day. round to the nearest tenth (if necessary).
Answer
Explanation:
Step1: Identify the decay - formula
The formula for exponential decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $P = 1300$ grams, $r=0.14$, and $t = 10$ (since we want the amount at the start of the 11th day, so 10 days have passed).
Step2: Substitute the values into the formula
$A=1300\times(1 - 0.14)^{10}$. First, calculate $1-0.14 = 0.86$. Then, $(0.86)^{10}\approx0.22137$.
Step3: Calculate the final amount
$A = 1300\times0.22137\approx287.8$.
Answer:
$287.8$ grams