what formula would you use to calculate the mass of fermium - 253 remaining after d days?\n$f(d)=400(0.833)^d…

Explanation:

Step1: Recall radioactive - decay formula

The general formula for radioactive decay is $f(t)=N_0\cdot r^t$, where $N_0$ is the initial amount, $r$ is the decay factor, and $t$ is the time. In this case, assume the initial amount of fermium - 253 is $N_0 = 400$, and $t = d$ (number of days). The decay factor $r$ is between $0$ and $1$. Without specific half - life information for fermium - 253, we assume this is a multiple - choice problem based on known decay characteristics. The half - life of fermium - 253 is about 3 days. The decay factor $r$ for a radioactive substance with half - life $T_{1/2}$ is given by $r = 2^{-\frac{1}{T_{1/2}}}$. For $T_{1/2}=3$ days, $r = 2^{-\frac{1}{3}}\approx0.794$.

Step2: Identify the correct formula

Substituting $N_0 = 400$ and $r\approx0.794$ into the radioactive - decay formula $f(d)=N_0\cdot r^d$, we get $f(d)=400(0.794)^d$.

Answer:

$f(d)=400(0.794)^d$