Question

A grey squirrel population was introduced in a certain county of Great Britain 30 years ago. Biologists observe that the population doubles every 6 years, and now the population is 100,000. what is the formula

Answer 1

Answer:

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

Step-by-step explanation:

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

$\frac{n_{t+6}}{n_{t}} = 2$ (1)

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

$\frac{n_{6}}{n_{o}} \cdot \frac{n_{12}}{n_{6}}\cdot \frac{n_{18}}{n_{12}}\cdot \frac{n_{24}}{n_{18}}\cdot \frac{n_{30}}{n_{24}} = 2^{5}$

$n_{30} = 2^{5}\cdot n_{o}$

$n_{o} = \frac{n_{30}}{2^{5}}$ (2)

$n_{o} = \frac{100000}{2^{5}}$

$n_{o} = 3125$

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

$n = 3125\cdot 2^{\frac{t}{6} }$ (3)

Where:

$t$ - Time, measured in years.

$n$ - Population of gray squirrels.