Question

question 5 of 5 in a lab, a scientist is running an experiment on a sample of radioactive particles. she observes that each day, half of the current number of particles disappears. if she wants to have 2 particles of the original sample left on the 5th day, what is the minimum number of particles she should start with? a 8 b 10 c 16 d 32

Explanation:

Step1: Identify the decay formula

The formula for radioactive - decay is $N = N_0(\frac{1}{2})^n$, where $N$ is the final amount of particles, $N_0$ is the initial amount of particles, and $n$ is the number of time - periods. Here, $n = 5$ (5 days) and $N\geq2$.

Step2: Rearrange the formula to solve for $N_0$

We have $N = N_0(\frac{1}{2})^n$, so $N_0=N\times2^n$.

Step3: Substitute the values of $N$ and $n$

Substitute $N = 2$ (the minimum number of particles we want to have left) and $n = 5$ into the formula $N_0=N\times2^n$. Then $N_0=2\times2^5$.
Using the rule of exponents $a^m\times a^n=a^{m + n}$, we get $N_0=2^{1 + 5}=2^6 = 32$.

Answer:

D. 32