Answer: 2023
Step-by-step explanation:
Since, the initial population of the city is 55,210,
And, it is declining at a rate of 1.09%.
Thus, the function that shows the population after x years since 2010 is,
[tex]f(x) = 55210(1-\frac{1.09}{100} )^x[/tex]
[tex]f(x) = 55210(1-0.0109)^x[/tex]
[tex]f(x) = 55210(0.9891)^x[/tex]
If the population of town is 48000 in x years.
⇒ [tex] 55210(0.9891)^x= 48000[/tex]
⇒ [tex] (0.9891)^x= 0.869407715993[/tex]
⇒ [tex]x = 12.769[/tex]
Therefore, after 12.769 years the population of town will be equals to 48,000
⇒ After 12.770 years the population will first be below 48,000.
⇒ After approx 13 years the population will first below 48,000.
⇒ Around 2023 the population will be first below 48,000.
