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Calculate the residence time of sodium.
[tex]\[ U \sec T=\frac{m}{f} \][/tex]

\begin{tabular}{|l|c|c|}
\hline & \begin{tabular}{c}
Mass [tex]$m$[/tex] \\
(tons)
\end{tabular} & \begin{tabular}{c}
Flow rate, [tex]$f$[/tex] \\
(tons/year)
\end{tabular} \\
\hline Sodium & [tex]$2.8 \times 10^{13}$[/tex] & [tex]$3.5 \times 10^5$[/tex] \\
\hline
\end{tabular}

Zach is investigating the residence time of sodium in seawater. According to Zach's data table, the residence time of sodium written in scientific notation is [tex]$\square$[/tex] [tex]$\times 10$[/tex] [tex]$\square$[/tex] years.


Sagot :

To find the residence time of sodium in sea water, we use the formula:

[tex]\[ T = \frac{m}{f} \][/tex]

where:
- [tex]\( m \)[/tex] is the mass of sodium in tons,
- [tex]\( f \)[/tex] is the flow rate of sodium in tons per year.

Given:
- Mass of sodium, [tex]\( m = 2.8 \times 10^{13} \)[/tex] tons,
- Flow rate, [tex]\( f = 3.5 \times 10^5 \)[/tex] tons/year.

First, we calculate the residence time [tex]\( T \)[/tex]:

[tex]\[ T = \frac{2.8 \times 10^{13}}{3.5 \times 10^5} \][/tex]

Simplifying this fraction:

[tex]\[ T = \frac{2.8}{3.5} \times \frac{10^{13}}{10^5} \][/tex]

[tex]\[ T = 0.8 \times 10^{8} \][/tex]

So, the residence time of sodium is:

[tex]\[ T = 0.8 \times 10^{8} \text{ years} \][/tex]

Therefore, the residence time of sodium written in scientific notation is [tex]\( 0.8 \times 10^8 \)[/tex] years.

In the given placeholders:

- The first blank should be filled with [tex]\( 0.8 \)[/tex],
- The second blank should be filled with [tex]\( 8 \)[/tex].

Thus, the complete answer is [tex]\( \mathbf{0.8} \times 10^{\mathbf{8}} \)[/tex] years.