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Calc word problem

  1. Sep 11, 2013 #1

    ufs

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    1. The problem statement, all variables and given/known data
    "1. The net change, C, in the energy level of a forging animal over a period of time t is equal to the energy intake, I, minus the energy expended, E: C= I-E
    Suppose that the energy intake (per unit time, j>0, is a constant. Then, over a time interval t, the total energy intake is I=jt.
    Further, suppose that B is the basal metabolic rate, and f is the energy required for foraging activity per unit time t, (where B, f>0 are constants). Then the total energy required to forage for time t is
    E= ft+B.

    a) Determine the time at which energy intake I balances energy spent, E i.e the time at which the net change in the energy level is zero.

    b) What conditions must be satisfied by the constants f and j (other than f,j>0) defined above for your answer to be biologically meaningful?

    c)Explain your answer in (b): what is this saying about the foraging?



    2. Relevant equations



    3. The attempt at a solution

    a) C= I-E
    0=I-E
    0=(jt)-E
    E/j=t

    b) Im not sure what it wants but this is what I did randomly.

    E-B/t=f and I/t=j

    c) Not sure on what to say due to (b)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 12, 2013 #2

    haruspex

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    The wording is certainly confusing.
    I think there are two time variables implied. One is for a period of existence, while the other is for a period of foraging within that. The first mention of 't' is for existence, while the rest are for foraging (the period of existence now being taken as 1). Thus, although B is described as a rate, it appears in the equation as a quantity of energy (having been multiplied by a unit period of existence).
    To untangle this, let's introduce T as a period of existence, and let h be the fraction of time spent foraging. Thus t = hT. Presumably the energy intake rate, j, only applies while foraging.
    We now have that the average rate of expending energy is B+hf, while the average rate of obtaining energy is hj. To put it another way, in time T, energy intake is jt = hjT, while energy expenditure is BT+ft = BT + hfT.
    Does that help?
     
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