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anonymous

  • 5 years ago

The rate of growth of a tree is calcuated ltaewaccording to the formua : dh/dt = 2+ 1/2t raised to the power of a half (1/2) where h is the height of the tree in metres and t is time in years. a) How much does the tree grow between the first and the fourth year? b) How much does the tree grow between the fourth and ninth year?

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  1. anonymous
    • 5 years ago
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    Is your 't' raised to the power of 1/2?

  2. anonymous
    • 5 years ago
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    yes

  3. anonymous
    • 5 years ago
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    You have to integrate this to find h as a function of t, then find the heights at various times and just do what the question asks you to do. I'll integrate it for you if you're unsure.

  4. anonymous
    • 5 years ago
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    ? k, guess not...

  5. anonymous
    • 5 years ago
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    thanks you can intergrate as i am unsure

  6. anonymous
    • 5 years ago
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    Before I do that, I need you to verify your expression for the derivative of h with respect to t:\[\frac{dh}{dt}=2+\frac{1}{2t^{1/2}}\]

  7. anonymous
    • 5 years ago
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    Correct

  8. radar
    • 5 years ago
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    H=2t+4t^1/2+C, since you are wanting the change in heighth I don't thin C is important and letting C=0 at first year 2+4 = 6 at 4th year 8+8= 16 for 10 ft of growth. for 9th yr. 18=12=30 for an additional 14 ft of growth. This is more or less a swag and I would wait for lokisan for the solution, but, does this come close to what you think it would be?

  9. anonymous
    • 5 years ago
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    I would say, since when you integrate, you end up with a constant, that constant disappears when you're dealing with differences (as in a definite integral), and since we'd be calculating height between two years, we can just write,\[h(t_2)-h(t_1)=\int\limits_{t_1}^{t_2}2+\frac{1}{2}t^{-1/2}dt=2t+t^{1/2}|_{t_1}^{t_2}=2t_2+{t_2}^{1/2}-2t_1-{t_1}^{1/2}\]

  10. anonymous
    • 5 years ago
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    So, between first and fourth year:\[h(4)-h(1)=2.4+\sqrt{4}-2.1-\sqrt{1}=10-3=7\]

  11. anonymous
    • 5 years ago
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    Between fourth and ninth,\[h(9)-h(4)=2.9+3-2.4-2=21-10 = 11\]

  12. anonymous
    • 5 years ago
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    metres...

  13. radar
    • 5 years ago
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    Well the swag was close, but no cigar!lol

  14. anonymous
    • 5 years ago
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    Hehe, it was your constant. You were right about it not being important, though.

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