Answer:

The formula for the gray squirrel population is [tex]n = 3125\cdot 2^{\frac{t}{6} }[/tex].

Step-by-step explanation:

The statement indicates that gray squirrel population increases geometrically, population is doubled every 6 years. That is:

[tex]\frac{n_{t+6}}{n_{t}} = 2[/tex] (1)

If the population after 30 years is 100000, then we construct the following relationship:

[tex]\frac{n_{6}}{n_{o}} \cdot \frac{n_{12}}{n_{6}}\cdot \frac{n_{18}}{n_{12}}\cdot \frac{n_{24}}{n_{18}}\cdot \frac{n_{30}}{n_{24}} = 2^{5}[/tex]

[tex]n_{30} = 2^{5}\cdot n_{o}[/tex]

[tex]n_{o} = \frac{n_{30}}{2^{5}}[/tex] (2)

[tex]n_{o} = \frac{100000}{2^{5}}[/tex]

[tex]n_{o} = 3125[/tex]

A geometric progression for the grey squirrel population is defined by the following formula:

[tex]n = 3125\cdot 2^{\frac{t}{6} }[/tex] (3)

Where:

[tex]t[/tex] – Time, measured in years.

[tex]n[/tex] – Population of gray squirrels.