Question

The half-life of a radioactive kind of tin is 10 days. If you start with 66,048 grams of it, how much will be left after 50 days?

Answer 1

To determine how much of the radioactive tin will be left after 50 days, we can use the formula for exponential decay based on half-life:

\[
N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}
\]

where:
- \( N(t) \) is the remaining quantity after time \( t \),
- \( N_0 \) is the initial quantity,
- \( T_{1/2} \) is the half-life,
- \( t \) is the time elapsed.

In this case:
- \( N_0 = 66,048 \) grams,
- \( T_{1/2} = 10 \) days,
- \( t = 50 \) days.

First, we calculate how many half-lives have passed in 50 days:

\[
\text{Number of half-lives} = \frac{t}{T_{1/2}} = \frac{50 \text{ days}}{10 \text{ days}} = 5
\]

Now, we can substitute this into the formula:

\[
N(50) = 66,048 \left(\frac{1}{2}\right)^{5}
\]

Calculating \( \left(\frac{1}{2}\right)^{5} \):

\[
\left(\frac{1}{2}\right)^{5} = \frac{1}{32}
\]

Now substituting this back into the equation:

\[
N(50) = 66,048 \times \frac{1}{32} = \frac{66,048}{32} = 2,064
\]

Therefore, the amount of radioactive tin left after 50 days is:

\[
\boxed{2,064} \text{ grams}
\]

Answer 2

A video posted on the internet is becoming very popular, and the total number of views is increasing by 30% every hour. If the video currently has 11,882 views, how many views will it have in 3 hours?
If necessary, round your answer to the nearest whole number.