Respuesta :
Answer:
7th Month
Step-by-step explanation:
The number of hectares of Lucia's land grows arithmetically by 5 hectares each month.
Whereas, the number of hectares of Maria's land grows geometrically with a common ratio of 1.4 every month.
Writing this as sequence expressions:
For Lucia,
First term, a=11 hectares
Common difference, d=5
Therefore:
[tex]T(n)=a+(n-1)d[/tex]
[tex]11+5(n-1)=11+5n-5\\=6+5n[/tex]
For Maria,
First term, a=6 hectares
Commons ratio=1.4
[tex]T(n)=ar^{n-1}\\=6*1.4^{n-1}[/tex]
Next, we compute and compare the results for values of n of these two equations:
[tex]Lucia, T(n)=6+5n[/tex]
[tex]Maria,T(n)=6*1.4^{n-1}[/tex]
[tex]Lucia, T(1)=6+5=11[/tex]
[tex]Maria,T(1)=6*1.4^{1-1}=6[/tex]
[tex]Lucia, T(2)=6+5(2)=16[/tex]
[tex]Maria,T(2)=6*1.4^{2-1}=8.4[/tex]
[tex]Lucia, T(3)=6+5(3)=21[/tex]
[tex]Maria,T(3)=6*1.4^{3-1}=11.76[/tex]
[tex]Lucia, T(4)=6+5(4)=26[/tex]
[tex]Maria,T(4)=6*1.4^{4-1}=16.56[/tex]
[tex]Lucia, T(5)=6+5(5)=31[/tex]
[tex]Maria,T(5)=6*1.4^{5-1}=23.05[/tex]
[tex]Lucia, T(6)=6+5(6)=36[/tex]
[tex]Maria,T(6)=6*1.4^{6-1}=32.27[/tex]
[tex]Lucia, T(7)=6+5(7)=41[/tex]
[tex]Maria,T(7)=6*1.4^{7-1}=45.18[/tex]
Therefore, in the seventh month, Maria's land will exceed that of Lucia.
