Respuesta :
Answer:
The population will be of 2400 in 36 years.
Step-by-step explanation:
The equation for the population of plants after t years follows the following format:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the initial amount of plants and r is the yearly rate which it increases.
Assuming that the initial population is 300
This means that P(0) = 300.
The doubling time of a population of plants is 12 years.
This means that P(12) = 2*300 = 600.
We use this to find r.
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]600 = 300(1+r)^{t}[/tex]
[tex](1+r)^{12} = 2[/tex]
[tex]\sqrt[12]{(1+r)^{12})} = \sqrt[12]{2}[/tex]
[tex]1 + r = 1.05946[/tex]
So
[tex]P(t) = 300(1.05946)^{t}[/tex]
How large will the population be in 36 years
This is P(36)
[tex]P(t) = 300(1.05946)^{36} = 2400[/tex]
The population will be of 2400 in 36 years.
The population will be = 2400 after 36 years
Calculation of population after 36 Years
Given : Population doubles in 12 years ; current population = 300
So, after 12 years, population = 300 x 2 = 600
After more 12 years, ie total 24 years, population = 600 x 2 = 1200
After further 12 years, ie total 36 years, population = 1200 x 2 = 2400
To learn more about Population Growth, refer https://brainly.com/question/12228859?referrer=searchResults
