Question

A town has a population that is modeled approximately by Px=275.5ln x+ 1 + 12, 573 where x is years after 2014. When do we expect the population to reach 13,000 citizens?

Answer 1

We expect the population to reach 13,000 citizens in 2026.

The question asked when the population of the town will reach 13,000. We were given the equation Px=275.5ln x+ 1 + 12, 573 that approximates the population of the town x years after 2014. Plugging in 13,000 for Px, we get:

13,000=275.5ln x+ 1 + 12, 573

We are solving 275.5ln x+ 1 + 12, 573 = 13,000 for x.

275.5ln x+ 1 = 427

275.5ln x = 426

ln x = 426/275.5

x = exp(426/275.5)

x = 12,225.37

2014 + 12,225.37 = 2026.37 years

x = 2026.37 years after 2014 which is in approximately 2026.37 years.

So the answer is 2026