Question

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?

Answer 1

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,

$f(x) = 55210(1-\frac{1.09}{100} )^x$

$f(x) = 55210(1-0.0109)^x$

$f(x) = 55210(0.9891)^x$

If the population of town is 48000 in x years.

⇒ $55210(0.9891)^x= 48000$

⇒ $(0.9891)^x= 0.869407715993$

⇒ $x = 12.769$

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.