Answer:
2023 rabbits
Step-by-step explanation:
The exponential model consists of the following expression:
[tex]y = A \cdot r^{t}[/tex]
Where:
[tex]A[/tex] - Initial population.
[tex]r[/tex] - Increase rate.
[tex]t[/tex] - Time
[tex]y[/tex] - Current population.
The initial population and increase rate are, respectively:
[tex]1200 = A \cdot r^{0}[/tex]
[tex]A = 1200[/tex]
[tex]1700 = 1200 \cdot r^{4}[/tex]
[tex]r^{4} = \frac{1700}{1200}[/tex]
[tex]r^{4} = \frac{17}{12}[/tex]
[tex]r = \sqrt[4]{\frac{17}{12} }[/tex]
[tex]r \approx 1.091[/tex]
The exponential model that predicts the population of rabbits is:
[tex]y = 1200\cdot 1.091^{t}[/tex]
Lastly, the expected population for the year 1996 is:
[tex]y = 1200\cdot 1.091^{6}[/tex]
[tex]y\approx 2023.624\,rabbits[/tex]
