Consider a population that grows to the recursive rule Pn= Pn-1 + 50, with initial population Po = 200 (a) Use the recursive for

Question

Consider a population that grows to the recursive rule Pn= Pn-1 + 50,
with initial population Po = 200
(a) Use the recursive formula to find: p1 and p2
(b) Find an explicit formula for the population.
(c) Use the explicit formula to find P60

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Thành Công 2 weeks 2021-08-29T00:08:11+00:00 1 Answers 0 views 0

Answers ( )

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    2021-08-29T00:10:01+00:00

    Answer:

    a)   P₁  = 250 and    P₂ = 300

    b) The explicit formula   Pₙ = 150+ 50 n

    c)  P_{60}  = 3150

    Step-by-step explanation:

    Step(i):-

    Given that Pₙ = pₙ₋₁ +50 and P₀ = 200

    Put n =1

             P₁ = P₀+50 = 200+50 = 250

    Put n =2

             P₂ = P₁+50 = 250+50 = 300

    Put n=3

           P₃ = P₂+50 = 300+50 = 350

    and so on

    The sequence     200,250,300,350,..

    Step(ii):-

    The sequence     200,250,300,350,.. is an arithmetic sequence

    The explicit formula

           Pₙ = a+(n-1)d

           Pₙ = 200+(n-1)50

           Pₙ = 200+ 50 n -50

            Pₙ = 150+ 50 n

    The explicit formula   Pₙ = 150+ 50 n

    c)

    The n^{th} term of the sequence

           Pₙ = 150+ 50 n

    put n=60

          P_{60} = 150 + 50 (60) = 3150

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