in 2010 , a city's population was 55,210 and it was declining at a rate of 1.09% each year. which is the best prediction for when the city's population will first be below 48,000?
Accepted Solution
A:
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.