Question

A species of animal is discovered on an island. suppose that the population size p(t) of the species can be modeled by the following function, where time t is measured in years.

P(t) =800/1+ 3e^-0.29t.
Find the initial population size of the species and the population size after 10 years. Round your answers to the nearest whole number as necessary. a) 550
b) 620
c) 684
d) 720

Answer 1

The initial population size is 200 and the population size after 10 years is approximately 684.

Step-by-step explanation:

The initial population size of the species can be found by substituting t = 0 into the population function.

So, P(0) = 800 / (1 + 3e^(-0.29 * 0)).

This simplifies to P(0) = 800 / (1 + 3e^0), which becomes P(0) = 800 / (1 + 3 * 1).

Thus, the initial population size is P(0) = 800 / 4 = 200.

The population size after 10 years can be found by substituting t = 10 into the population function.

So, P(10) = 800 / (1 + 3e^(-0.29 * 10)).

This simplifies to P(10) = 800 / (1 + 3e^(-2.9)).

Using a calculator, we can find that P(10) ≈ 684.