Question

See attached pic for problem. Has parts A and B

Answer 1

Step-by-step explanation

Part A

The formula for an exponential decay model is given as:

`y=C(1-r)^t`

Where C is the initial amount and r is the decay rate and t is the time.

Given that the amount of radon has a half-life of 3.8 days, it implies that the original amount will decay to half of itself in 3.8 days. Therefore, we will have

`\begin{gathered} (1)/(2)R_0=R_0(1-r)^(3.8) \\ (1)/(2)=(1-r)^(3.8) \\ \sqrt[3.8]{0.5}=1-r \\ r=1-\sqrt[3.8]{0.5} \\ r=0.1667 \\ r=16.7\text{ \%} \end{gathered}`

Answer: The daily decay rate is 16.7% per day

Part B

We can find the formula below;

`\begin{gathered} R=R_0(1-0.1667)^t \\ R=R_0(0.833)^t \end{gathered}`

Answer: Option A

Part C

The percentage of radon after 13 days will be gotten with the formula below.

`\frac{Amount\text{ after 13 days}}{Original\text{ amount}}*100`

Therefore,

`\begin{gathered} (R_0(0.833)^(13))/(R_0)*100 \\ =9.30\text{\%} \end{gathered}`

Answer: 9.30%