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,
![f(x) = 55210(1-\frac{1.09}{100} )^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2055210%281-%5Cfrac%7B1.09%7D%7B100%7D%20%29%5Ex)
![f(x) = 55210(1-0.0109)^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2055210%281-0.0109%29%5Ex)
![f(x) = 55210(0.9891)^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2055210%280.9891%29%5Ex)
If the population of town is 48000 in x years.
⇒ ![55210(0.9891)^x= 48000](https://tex.z-dn.net/?f=%2055210%280.9891%29%5Ex%3D%2048000)
⇒ ![(0.9891)^x= 0.869407715993](https://tex.z-dn.net/?f=%20%280.9891%29%5Ex%3D%200.869407715993)
⇒ ![x = 12.769](https://tex.z-dn.net/?f=x%20%3D%2012.769)
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.