Respuesta :
Answer:
The present population of the country is 26,000.
[tex]y=a(1+r)^{x}[/tex]
The growth rate is approximately 12%.
The population 5 years from today will be 45,821.
Step-by-step explanation:
(1)
The present population of the country is 26,000.
(2)
It is provided that the number of people living in a country is increasing each year exponentially.
Then the exponential growth function can be used to describe the situation.
The exponential growth function is:
[tex]y=a(1+r)^{x}[/tex]
Here,
y = final value
a = initial value
r = growth rate
x = time
(3)
It is provided that x = 5 years ago the population was a = 15,000 and at present the population is y = 26,000.
Compute the value of r as follows:
[tex]y=a(1+r)^{x}[/tex]
[tex]26000=15000\times (1+r)^{5}[/tex]
[tex](1+r)=[\frac{26000}{15000}]^{1/5}[/tex]
[tex]1+r=1.1163[/tex]
[tex]r=0.1163\\r\approx 0.12[/tex]
Thus, the growth rate is approximately 12%.
(4)
Compute the population 5 years from today as follows:
[tex]y=a(1+r)^{x}[/tex]
[tex]=26000\times (1+0.12)^{5}\\\\=26000\times 1.762342\\\\=45820.892\\\\\approx 45821[/tex]
Thus, the population 5 years from today will be 45,821.
