Respuesta :
Answer:
Third option i.e. A. [tex]2700(1.04)^x[/tex] and B. About 4,323 people
Step-by-step explanation:
We are given that,
Initial population of the town = 2,700
The rate of growth = 4% = 0.04
Part A: Since, the equation for the growth is given by,
Population growth = [tex]P(1+r)^x[/tex], where P is the initial population, r is the rate of growth and x is the time period of growth.
We have, according to the question,
Population growth = [tex]2700(1+0.04)^x[/tex]
i.e. Population growth = [tex]2700(1.04)^x[/tex]
Thus, the equation for the population growth is [tex]2700(1.04)^x[/tex].
Part B: Now, it is required to find the population after 12 years i.e. x= 12.
So, we have,
Population = [tex]2700(1.04)^x[/tex]
i.e. Population = [tex]2700(1.04)^{12}[/tex]
i.e. Population = [tex]2700\times 1.601032[/tex]
i.e. Population = 4,323
Hence, the population after 12 years is 4,323 people.
Thus, the third option is correct.
Answer:
Equation to model the population growth is [tex]y = 2700(1.04)^{x}[/tex] and the population after 12 years is 4323 (Approx) .
Step-by-step explanation:
The exponential increase function is given by
[tex]y = a (1 + r)^{x}[/tex]
Where a is the initial value, r is the rate of interest in the decimal form and x is the time in years .
As given
Suppose the population of a town is 2,700 and is growing 4% each year.
a = 2700
4% is written in the decimal form .
[tex]= \frac{4}{100}[/tex]
= 0.04
r = 0.04
Thus the equation becomes for population growth.
[tex]y = 2700(1 + 0.04)^{x}[/tex]
[tex]y = 2700(1.04)^{x}[/tex]
As given
x = 12 years
Put in the formula
[tex]y = 2700(1.04)^{12}[/tex]
[tex]y = 2700\times 1.60103[/tex]
y = 4323 (Approx)
Therefore the population after 12 years is 4323 (Approx) .
