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4. If you present a flash of light to a salamander rod (a type of photoreceptor) then the photocurrent of the rod first rises and then decays. Here's some typical experimental data, taken from Hamer RD, Vis Neurosci. (2000) Sep-Oct;17(5):679-99. 40 - -Data from salamander rods A very simple model 30 Photocurrent (PA) 20- 10 - 0 0 50 150 200 100 Time (sec) The red curves are a very simple model of the photocurrent, R, given by R(t) = Rot"e-kt for some constants Ro > 0, n (a positive integer) and k > 0. Use this model to answer the following questions. (a) When does the peak occur? (b) What is the value of R at the peak? 5. When you take a single dose of an antibiotic, or other kind of medication, the concentration, C, of drug in your blood stream is often well described by the equation C(t) = Cote-kt, for some constants Co and k. Furthermore, the rate, r, at which that drug reacts can often be well modelled by a Michaelis- Menten equation с r(C) = Vmax Km+C' for some constants Vmax >0 and Ky > 0. (a) Since r is a function of C, and C is a function of t, this means that r is a function of t. Using the chain rule, calculate how fast the reaction rate is changing as a function of time, i.e., calculate r(t). Plot the rate of change the reaction rate, as a function of time. (b) Why would we care about how fast the reaction rate is changing?