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11 June, 07:19

Write an explicit rule for the sequence that models this situation:

the wolf population in a local wildlife area is currently 12. due to a new conservation effort, conservationists hope the wolf population will increase by 2 each year for the next 50 years. assume the plan will be successful

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Answers (2)
  1. 11 June, 08:56
    0
    Step-by-step explanation:

    The population will increase by 2 each year. This means that the sequence is an arithmetic progression.

    The formula for determining the sum of n terms of an arithmetic sequence is expressed as

    Sn = n/2[2a + (n - 1) d]

    Where

    n represents the number of terms in the arithmetic sequence.

    d represents the common difference of the terms in the arithmetic sequence.

    a represents the first term of the arithmetic sequence.

    From the information given,

    a = 12

    d = 2 years

    Therefore, the explicit rule for the sequence that models this situation: would be

    Sn = n/2[2 * 12 + (n - 1) 2]

    Sn = n/2[24 + 2 (n - 1) ]

    For the next 50 years, n = 50

    S50 = 50/2[2 * 12 + (50 - 1) 2]

    S50 = 25[24 + 98)

    S50 = 3050
  2. 11 June, 09:15
    0
    n = 12 + 2t,

    where t is less than or equal to 50

    Step-by-step explanation:

    Let n be the number or wolves and t be the number of years after the conservation efforts began.

    n = 12 + 2t,

    where t is less than or equal to 50
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