Question

TASK 3= 50 POINTSSS

in the year 1995, the population of a town was recorded as 25,400 people. each year since 1995, the population has increased non average by 11% each year.



during what year will the population of the town in task 3 first exceed that of the city in task 2? show all your work and explain your steps.

in task 2 was , f(0)=501170

Answer 1

`After \: 1 \: year:25400 + 25400 * 11\% = 25400 + 25400 * 0.11 = 25400(1 + 0.11) = 25400 * 1.11 \\ After \: 2 \: year:25400 * {1.11}^(2) \\ After \: x \: year:25400 * {1.11}^(x) \\ We\: have\: an\: inequality:25400 * {1.11}^(x) > 501170 \\ \Leftrightarrow {1.11}^(x) > (50117)/(2540)\\ \Leftrightarrow x > \log _(1.11)((50117)/(2540)) \\ \Leftrightarrow x>29\\\Rightarrow After\: 29\: years`