Respuesta :
Answer:
59049.
Step-by-step explanation:
It is given that, 2 years later, two years ago, the population of this same city was 81,000 and today it is 65,610.
So, graph passing through (2,81000) and (-2,65610).
The general exponential function is
[tex]y=ab^x[/tex]
where, a is initial value or present year population and b is growth factor.
Since graph passing through (2,81000) and (-2,65610), therefore the above equation must be satisfied by these points.
[tex]81000=ab^2[/tex] ...(1)
[tex]65610=ab^{(-2)}[/tex] ...(2)
Multiplying (1) and (2), we get
[tex]81000\times 65610=ab^2\times ab^{-2}[/tex]
[tex]5314410000=a^2[/tex]
Taking square root on both sides.
[tex]72900=a[/tex]
Substitute a=72900 in (1).
[tex]81000=72900b^2[/tex]
[tex]\dfrac{81000}{72900}=b^2[/tex]
[tex]\dfrac{10}{9}=b^2[/tex]
Taking square root on both sides.
[tex]\dfrac{\sqrt{10}}{3}=a[/tex]
So, the population function is
[tex]y=72900\left(\dfrac{\sqrt{10}}{3}\right)^x[/tex]
Substitute x=-4 in the above equation, to find the population of four years ago.
[tex]y=72900\left(\dfrac{\sqrt{10}}{3}\right)^{-4}[/tex]
[tex]y=72900(0.81)[/tex]
[tex]y=59049[/tex]
Therefore, the population of four years ago is 59049.
