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Changing the water levels of a lake

  1. Nov 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Attached problem

    2. Relevant equations
    Anti-derivatives, linear approx. F(a)=f(a)+F'(a)(x-a)

    3. The attempt at a solution
    I'm stuck on the first part, I think (w')^-1(1)= W which is 1. It seems too easy... and for part c I'm having trouble finding the equation for the line. I figured that if I graph it on my calculator and use a regression test to find the equation
     

    Attached Files:

    Last edited: Nov 9, 2015
  2. jcsd
  3. Nov 9, 2015 #2

    berkeman

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    Staff: Mentor

    The attachment is way too zoomed out for me to read. Can you type the problem statement into the forum? That would help... :smile:
     
  4. Nov 9, 2015 #3
    updated it, sorry for that.
     
  5. Nov 10, 2015 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Is your question just the part that is checked: "(b) Explain what item iv means in terms of the city, lake, and IES budget"?

    Item iv is "[itex](w^{-1})'(1)[/itex]". Since w(t) is the depth of water in the lake at time t, [itex]w^{-1}(x)[/itex] is the time at which the level of the lake is x. Then [itex](w^{-1})'(x)[/itex] is the rate at which time for the water to decrease amount x is changing.
     
  6. Nov 10, 2015 #5
    My question is on part a, I'm confused what(w')^-1(1) is. Thank you for help with part B :)
     
    Last edited: Nov 10, 2015
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