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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

Respuesta :

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

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