The net change, C, in the energy level of a foraging animal over a period of tim

Question

The net change, C, in the energy level of a foraging 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 (in calories) per unit time, j > 0, is 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 satised by the constants dened above for your answer to
be biologically meaningful?
(c) Explain your answer in (b): what is this saying about the foraging?

Explanation / Answer

(a) I = jt=E = ft + B ==> t = B/(j-f) (b)( B > 0 and j > f ) (c) energy required for foraging must be always less than energy intake (in calories) per unit time

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