Question 46 2.5 Sequential Limits155b. Determine how large x needs to be to ensure thatf (x) is within 0.01 of L.46. The following equation is used to calculate the aver-age firing rate f of a neuron (in spikes per second) asa function of the concentration x of neurotransmit-44. The von Bertalanffy growth curve is used to describehow the size L(usually in terms of length) of an ani-mal changes with time. The curve is given byters perfusing its synapses.20 e3xf(x) =L() — а(1 — е -bе -о)2.1 + e3xFind the horizontal asymptote; then find the valuesof x such that f(x) is within 0.5% of its asymptoticwhere t measures time after birth and a, b, and toare positive parameters. We will derive this curve inChapter 6. To better understand the meaning of theparameters to and b, carry out these steps.values.47. The following equation is used to calculate theaverage firing rate f of a neuron (in spikes persecond) as a function of the concentration x ofneurotransmitters perfusing its synapses.a. Evaluate L(to). What does this imply about themeaning of to?b. Find lim L(t). What does this limit say about thebiological meaning of a?16 e5xf(x) =3.2 + ебхc. Graph L(t) and discuss how an organism growsaccording to this curve.45. At the beginning of the twentieth century, sev-eral notable biologists, including G. F. Gause andT. Carlson, studied the population dynamics of yeast.For example, Carlson grew yeast under constantenvironmental conditions in a flask; he regularlymonitored their population densities.* In Chapter 6,we will show that the following function describestheFind the values of x such that f(x) is within 0.5% ofits asymptotic values.48. Compare the solutions obtained to Problems 46 and47 and decide which of these represents a tighteron-off switch of the neuron, that is, from firing at itsmaximum rate to being inactive. What do you con-clude in terms of which of the parameters a, b, and cin the functiongrowth of the population:аесх9.7417e0.53tf(x)b+ ecxN(t)1+0.01476e.531controls the narrowness of the range of x over whichon-off switching occurs? Note that this function iscalled the logistic function and will be encounteredin many different examples in upcoming chapters.where N(t) is the population density and t is time inhours. Find lim N(t) and discuss the meaning of thislimit.

The equation fx=20e3x2.1+e3x is used to calculate the average firing rate f of a neuron (in spikes…

46. The following equation is used to calculate the aver- age firing rate f of a neuron (in spikes per second) as a function of the concentration x of neurotransmit- ters perfusing its synapses. 20 e3x f(x) = 2.1 + e3x Find the horizontal asymptote; then find the values

46. The following equation is used to calculate the aver- age firing rate f of a neuron (in spikes per second) as a function of the concentration x of neurotransmit- ters perfusing its synapses. 20 e3x f(x) = 2.1 + e3x Find the horizontal asymptote; then find the values

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter87: An Introduction To G- And M-codes For Cnc Programming

Section: Chapter Questions

Problem 27A: Write a CNC G-code program to machine the part in the following figure, so that the tip of the tool...

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