Lucia and Maria are business women who decided to invest money by buying farm land in Brazil. They started their investments at the same time, and each month they buy more land. Lucia bought 111111 hectares of land in the first month, and each month afterwards she buys 555 additional hectares. Maria bought 666 hectares of land in the first month, and each month afterward her total number of hectares increases by a factor of 1.41.41, point, 4. In which month will Maria's amount of land first exceed Lucia's amount of land?

Answer:In 7th month.Step-by-step explanation:Let the number of months = x.It is given that Lucia bought 11 hectares of land in the 1st month and added 5 hectares each month after.Amount of land Lucia bought, [tex]L(x)=11+5(x-1)[/tex]Now, Maria bought 6 hectares of land in the 1st month and increases land by a factor of 1.4 each month after.Amount of land Maria bought, [tex] M(x)=6(1.4)^{x-1}[/tex]So, we will form the table for the values of the functions representing the lands,Months (x)               Lucia, [tex]L(x)=11+5(x-1)[/tex]      Maria, [tex]M(x)=6(1.4)^{x-1}[/tex]1                                              11                                             62                                             16                                           8.43                                            21                                           11.84                                            26                                          16.55                                            31                                           236                                            36                                          32.27                                            41                                           45.18                                            46                                           63.1So, we see that,In 7th month, Maria'a amount of land will exceed Lucia's amount of land.