Answer
The required model is \[P=\left( 0.000000000417 \right)\cdot {{\left( 1.021 \right)}^{t}}\]
Work Step by Step
The exponential model is defined as
\[P=a\cdot {{b}^{t}}\]
where \[P\] is the population of the particular year and \[t\] is the time point, \[a\text{ and }b\] are the regression coefficients.
The coefficients for the regression line are obtained as \[-9.38\] and 0.009 from which the regression coefficients for the exponential model are obtained.
The coefficients for the exponential model are calculated as
\[\begin{align}
& a={{10}^{\log \left( a \right)}} \\
& ={{10}^{-9.38}} \\
& =0.000000000417
\end{align}\]
and
\[\begin{align}
& b={{10}^{\log \left( b \right)}} \\
& ={{10}^{0.009}} \\
& =1.021
\end{align}\]
Therefore, the regression model is obtained as
\[P=\left( 0.000000000417 \right)\cdot {{\left( 1.021 \right)}^{t}}\]
