Question

Bismuth-210 has a half-life of about 6 days. After 21 days, how many milligrams of a1,220 mg sample will remain? Round answer to the nearest tenth place. If answerdoes not have tenths place use a zero so that it does.

Answer 1

Step 1:

In this question, we are given the following:

Bismuth-210 has a half-life of about 6 days.

After 21 days, how many milligrams of a 1,220 mg sample will remain?

Round answer to the nearest tenth place.

Step 2:

The details of the solution are as follows:

`\begin{gathered} We\text{ have that:} \\ 0.5\text{ = e}^(-6k) \\ Taking\text{ In of both sides, we have that:} \\ ln\text{ 0.5 = -6k} \\ That\text{ means that:} \\ k\text{ =}\frac{-ln\text{ 0. 5}}{6} \end{gathered}`
`Let\text{ the number to remain, A=1220e}^{-(-(ln0.5)/(6))(21)}`
`\begin{gathered} 107.83378\text{ mg} \\ \approx\text{ 107. 8 mg \lparen to the nearest tenth\rparen} \end{gathered}`

CONCLUSION:

The final answer is:

`107.\text{ 8 mg \lparen to the nearest tenth\rparen}`