Answer
shown below
Work Step by Step
(a)
Consider the given data:
\[\begin{align}
& \frac{16.24}{15.98}=1.02 \\
& \frac{16.50}{16.24}=1.02 \\
& \frac{16.76}{16.50}=1.02 \\
& \frac{17.03}{16.76}=1.02 \\
\end{align}\]
\[\begin{align}
& \frac{17.30}{17.03}=1.02 \\
& \frac{17.58}{17.30}=1.02 \\
& \frac{17.86}{17.58}=1.02 \\
& \frac{18.15}{17.86}=1.02 \\
\end{align}\]
\[\begin{align}
& \frac{18.44}{18.15}=1.02 \\
& \frac{18.80}{18.44}=1.02 \\
\end{align}\]
Take the geometric mean of the above outputs:
\[\frac{1.02+1.02+1.02+1.02+1.02+1.02+1.02+1.02+1.02+1.02}{10}=1.02\]
It is shown that the increase in the population of Florida is approximately geometric.
(b)
The general model for n successions is given by:
\[{{a}_{n}}=a{{\left( r \right)}^{n-1}}\]
Where,
‘a’is the first term of the series, r is the common geometric ratio between the terms and n is the number of terms.
(c)
The mathematical model created in the previous part is given as:
\[{{a}_{n}}=15.98{{\left( 1.02 \right)}^{n-1}}\]
By using the above formula for:
\[\begin{align}
& n=2030-2000 \\
& n=30, \\
& {{a}_{n}}=15.98{{\left( 1.02 \right)}^{30-1}} \\
& {{a}_{n}}=15.98{{\left( 1.02 \right)}^{29}}
\end{align}\]
\[\begin{align}
& {{a}_{n}}=15.98\left( 1.77 \right) \\
& {{a}_{n}}=28.38\text{ million} \\
\end{align}\]
