Question

A species of animal is discovered on an island. Suppose that the population size of the species can be modeled by the following function, where time t is measured in years. P(t) = 520/1 + 8e-0.3t Find the initial population size of the species and the population size after years.

Answer 1

Answer:

The initial population size is of 58.

The population size of the specie after t years is given by:

$P(t) = \frac{520}{1 + 8e^{-0.3t}$

Step-by-step explanation:

Population size of the specie:

The population size of the specie after t years is given by:

$P(t) = \frac{520}{1 + 8e^{-0.3t}$

Initial population size

This is P when $t = 0$, that is, $P(0)$. So

$P(0) = \frac{520}{1 + 8e^{-0.3*0} = \frac{520}{1+8} = \frac{520}{9} = 57.7$

Rounding to the nearest number, 58

The initial population size is of 58.