Question 19 (Mandatory) (1 point) A radioactive sample with an initial mass of 35 mg has a half-life of 3 days. Which of the following equations models the exponential decay for time, t, in days? a) A=35(2)^(1)/(3) b) A=35((1)/(2))^(1)/(3) c) A=35(2)^(3)/(2) d) A=35((1)/(2))^(3)/(2)

## Step 1: Calculate the fraction of the sample remaining after t days.<br />### The half-life is 3 days, meaning the sample halves every 3 days. After $t$ days, the number of half-lives that have passed is $\frac{t}{3}$. Therefore, the fraction of the sample remaining is $(\frac{1}{2})^{\frac{t}{3}}$.<br /><br />## Step 2: Determine the equation for the remaining mass.<br />### The initial mass is 35 mg. Multiply the initial mass by the fraction remaining to find the mass after $t$ days: $A = 35(\frac{1}{2})^{\frac{t}{3}}$.