Calculus

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A tree grows 2.80 m during the first year since it was planted. During each subsequent year the tree's growth is 85% of its growth the previous year.

a) Calculate to the nearest 0.001m, the growth of the tree in the fourth year.

Tn = ar^n-1
T4 = 2.80(0.85)^10-1
T4 = 2450
I don't get how to do this, the answer is wrong, its supposed to be 1.72m :\

Determine the first year in which the growth of the tree is less than half a metre.

  • Calculus -

    Where in the world did you get 10 in the 10-1
    should have been 4-1

    T4 = 2.8(.85)^3 = 1.719 or 1.72

    for growth to be .5

    .5 = 2.8(.85)^(n-1)
    divide by 2.8
    .17857.. = .85^(n-1)
    take log of both sides
    log (.17857..) = log [.85^(n-1)]
    log (.17857..) = (n-1)log [.85]
    n-1 = log (.17857..) / log [.85] = 10.6
    n = 11.6

    in year 11, growth = 2.8(.85)^10 = .5512
    in year 12, growth = 2.8(.85)^11 = .468

    so what do you think?

  • Calculus -

    So that would be Year 12.

  • Calculus -

    yes

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