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:2022

Explanation:

Answer 2

Answer: 2023

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-(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.