Question

3. Suppose a male and a female of a certain species of animal were taken to a deserted island. The population of this species quadruples (multiplies by 4) every year. Assume that the

animals have an abundant food supply and that there are no predators on the island.
a. What is an equation that can be used to model the population of the species?
b. What will the population of the species be after 5 years?
c.Write an equation to find how many years it will take for the population of the animals to exceed 1 million.
Find the number of years, either by using the equation or a table.

Answer 1

Explanation:

Since their current population is 2

And there Is no predator and also they have abundant food supply

Then

1a) An equation that can be used to model the population of the species is

= (2^2n+1) where n stand for the number of years that have passed by.

1b) their population after 5 years will be

2^((2*5)+1)

2^10+1

=2^11

Population after 5 years =2048

Answer 2

a) 2*4^n b)2048 c) n > 9.46578

Explanation:

The initial population was the two parents ( male and female)

After first year, the population quadruples = 2*4 = 8

After second year, the population = 2*4*4= 32

After third year, the population = 2" 4*4*4

After n number of years, the population = 2*4^n

b) after 5years, the population = 2*4^5 =2048

C) for the population to exceed 1million the equation becomes 2*4^n > 1 000 000

4^n > 500000, take log of both side

nlog4 > log 500000

n > log 500000/log(4) > 9.46578