In the year 2000 the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)^x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 118 million? Round your answer to the nearest year.​

Answer: The population reach 111 million in 2007.Step-by-step explanation:In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function [tex]f(x) = 100(1.0153)^x[/tex] gives the population, in millions, x years after 2000. Put f(x)=111 million.Then, [tex]111=100(1.0153)^x\\\\\Rightarrow\ (1.0153)^x=\dfrac{111}{100}=1.11\\\\\Rightarrow (1.0153)^x=1.11[/tex]Taking log on both the sides , we get[tex]x\log1.0153=\log1.11\\\\\Rightarrow\ x=\dfrac{\log1.11}{\log1.0153}=\dfrac{0.045323}{0.0066}=6.86712121212\approx7[/tex]Hence, the population reach 111 million in 2007 (approx).