Respuesta :
Using an exponential function, it is found that the present population of the country is of 5 million.
What is an exponential function?
It is modeled by:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial value and r is the growth rate, as a decimal.
Considering five years ago as the first year, we have that P(0) = 4, P(10) = 6.25, hence this is used to find r.
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]6.25 = 4e^{10r}[/tex]
[tex]e^{10r} = 1.5625[/tex]
[tex]\ln{e^{10r}} = \ln{1.5625}[/tex]
[tex]10r = \ln{1.5625}[/tex]
[tex]r = \frac{\ln{1.5625}}{10}[/tex]
[tex]r = 0.044629[/tex]
Then, the equation is:
[tex]P(t) = 4e^{0.044629t}[/tex]
The present moment is five years from the beginning, hence:
[tex]P(5) = 4e^{0.044629 \times 5} = 5[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
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The present population of the country is 4.9 million people
How to determine the present population?
Let x represent the number of years and y represents the population.
So, we have the following points:
(x,y) = (-5,4 million) and (5,6.25 million)
An exponential function is represented as:
[tex]y = ab^x[/tex]
So, we have:
[tex]4 = ab^{-5}[/tex]
[tex]6.25 = ab^{5}[/tex]
Divide both equations
[tex]b^{10} = 1.5626[/tex]
Take the 10th root of both sides
b = 1.05
Substitute b = 1.05 in [tex]6.25 = ab^{5}[/tex]
[tex]6.25 = a(1.05)^5[/tex]
Evaluate the exponent
6.25 = 1.276a
Divide both sides by 1.276
a = 4.9
Hence, the present population of the country is 4.9 million people
Read more about exponential functions at:
https://brainly.com/question/11464095
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