EXAMPLE $3$ The linear equation $C=1\mathrm{.}65429t-2938\mathrm{.}07$ models the average $C{O}_2,$ carbon dioxide, level $($measured in parts per million$)$ in the atmosphere at an observatory from $1980$ to $2008.$ Use the linear model to estimate the average $C{O}_2$ level for $1987$ and to predict the level for the year $2017.$ According to this model, when will the $C{O}_2$ level exceed $430$ parts per million?

SOLUTION Using $C=1\mathrm{.}65429t-2938\mathrm{.}07$ with $t=1987,$ we estimate that the average $C{O}_2$ level in $1987$ was

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$C(1987)=1\mathrm{.}65429$

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$|-2938\mathrm{.}07$~~$|$

$($rounded to two decimal

This is an example of interpolation because we have estimated a value between observed values.

With $t=2017,$ we get

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