the starting amount of radioactive iodine - 131 was 250 g. the half - life is 8 days. when leslie measured…

Answer:

C. 32

Explanation:

Step1: Recall half - life formula

$A = A_0(\frac{1}{2})^{\frac{t}{h}}$ where $A$ is the final amount, $A_0$ is the initial amount, $t$ is the time elapsed, and $h$ is the half - life. Given $A_0 = 250$ g, $A=15.625$ g, and $h = 8$ days. Substitute into the formula: $15.625=250(\frac{1}{2})^{\frac{t}{8}}$.

Step2: Simplify the equation

First, divide both sides by 250: $\frac{15.625}{250}=(\frac{1}{2})^{\frac{t}{8}}$. $\frac{15.625}{250}=\frac{15625}{250000}=\frac{1}{16}$, so $\frac{1}{16}=(\frac{1}{2})^{\frac{t}{8}}$. Since $\frac{1}{16}=(\frac{1}{2})^4$, we have $(\frac{1}{2})^4 = (\frac{1}{2})^{\frac{t}{8}}$.

Step3: Solve for $t$

Set the exponents equal: $4=\frac{t}{8}$. Multiply both sides by 8: $t = 32$ days.