In mammals, circadian rhythms (i.e., the rhythms that occur on the day/night cycle) are controlled by neurons in the suprachiasmatic nucleus of the hypothalamus. Fig. 5.19 shows a result from a model of circadian rhythms showing how the concentration (Vi

, in nM) of neurotransmitter produced by a typical neuron varies over a time period of a few days.

a. Estimate the maximal value of Vi (the units are in nanomolar, or nM). Just do this by eye; it doesn’t have to be very accurate.

b. Estimate the minimal value of Vi , again by eye.

c. Estimate the midpoint of the oscillation.

d. Estimate the period of the oscillation.

e. Now, note that the peak of the oscillation occurs at t = 2000 hours. From this, and using the estimates in parts (a), (b)
and

(c) above, write this oscillation as a cosine function.
That is, write Vi(t) = Acos(2π f (t − t0)) + V0, and determine what A, f , t0 and V0 need to be for your cosine function to look like the data.