Question 5 (4 pts):
A) (1 pt) Suppose you find an animal that only has three different olfactory receptors, each
expressed in a different neuron. These neurons appear to have limited variability in
firing rate, appearing to fire at either over 100 Hz (spikes/s) or are completely silent.
How many odors should this animal be able to detect?
B) (1) You find that the animal begins to express more variability in firing rate when it is
starved - under these circumstances, the firing rate of these olfactory neurons can be
over 90 Hz, between 50-75 Hz, 25-35 Hz, 5-15 Hz, or completely silent (less than 1 Hz).
Assuming this means that the neuron can adopt five possible firing rates, how many
different odorants might this animal be able to detect with its three olfactory neurons?
Assume that a chemically identical odorant delivered at two different concentrations is
considered a \"different\" odor.
C) (2 pts) If we assume that this animal with 3 olfactory neurons needs to discriminate
against 500 odorants, how many different firing modes would be necessary? Reminder
about logarithm rules - the information provided below is just an example to help you
with the math; it uses the numbers 2 and 4, which are not relevant to this problem set:
$2^4 = 16$
$\log_2(16) = 4$
$\log_b(c) = 1/(\log(b))$
