What is the first month in which Maria’s amount of land exceeds Lucia’s amount of land?

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What is the first month in which Maria’s amount of land exceeds Lucia’s amount of land?

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Evelyn 2 months 2021-10-12T07:24:36+00:00 1 Answer 0 views 0

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    2021-10-12T07:25:37+00:00

    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:

    T(n)=a+(n-1)d

    11+5(n-1)=11+5n-5\\=6+5n

    For Maria,

    First term, a=6 hectares

    Commons ratio=1.4

    T(n)=ar^{n-1}\\=6*1.4^{n-1}

    Next, we compute and compare the results for values of n of these two equations:

    Lucia, T(n)=6+5n

    Maria,T(n)=6*1.4^{n-1}

    Lucia, T(1)=6+5=11

    Maria,T(1)=6*1.4^{1-1}=6

    Lucia, T(2)=6+5(2)=16

    Maria,T(2)=6*1.4^{2-1}=8.4

    Lucia, T(3)=6+5(3)=21

    Maria,T(3)=6*1.4^{3-1}=11.76

    Lucia, T(4)=6+5(4)=26

    Maria,T(4)=6*1.4^{4-1}=16.56

    Lucia, T(5)=6+5(5)=31

    Maria,T(5)=6*1.4^{5-1}=23.05

    Lucia, T(6)=6+5(6)=36

    Maria,T(6)=6*1.4^{6-1}=32.27

    Lucia, T(7)=6+5(7)=41

    Maria,T(7)=6*1.4^{7-1}=45.18

    Therefore, in the seventh month, Maria’s land will exceed that of Lucia.

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45:7+7-4:2-5:5*4+35:2 =? ( )