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