22. The Nobel Prize in Physiology or Medicine in 1963 was shared by A.L. Hodgkin and A.F. Huxlleyin recognition of their model for the firing of neuronal synapses. They proposed that the open-ing/closing of certain ion channels in the neuron cell was govered by a combination of probabilistic"gating variables," each satisfying a differential equation that they expressed asdu(a + B)udtwith positive parameters a =show that all solutions converge to the same value as t → .[your choice], ß = [your choice] of numbers. Solve the equation and3du3 - (3-2)uathp= 3-uヒ

(2) Consider the provided question,

Answered: 2 2. The Nobel Prize in Physiology or…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Endocrinology In Section 2.10, we described Data Set BONEDEN.DAT concerning the effect of tobacco use on BMD. Note: 2.38-2.40 Involve computing a new variable C. Compute C using the formula given and then use STATA to produce the output requested. 2.38. For each pair of twins, compute the following for the lumbar spine: A = BMD for the heavier-smoking twin − BMD for the lighter-smoking twin = x1 − x2 B = mean BMD for the twinship = (x1 + x2)/2 C = 100% × (A/B) Derive appropriate descriptive statistics for C over the entire study population. 2.39. Suppose we group the twin pairs according to the difference in tobacco use expressed in 10 pack-year groups (0–9.9 pack-years/10–19.9 pack-years/20–29.9 pack-years/30–39.9 pack-years/40+ pack-years). Compute appropriate descriptive statistics, and provide a scatterplot for C grouped by the difference in tobacco use in pack-years 2.40. What impression do you have of the relationship between BMD and tobacco use based on Problem 2.39?
Clean Fossil Fuels. In the article, “Squeaky Clean Fossil Fuels” (New Scientist, Vol. 186, No. 2497, p. 26), F. Pearce reported on the benefits of using clean fossil fuels that release no carbon dioxide (CO2), helping to reduce the threat of global warming. One technique of slowing down global warming caused by CO2 is to bury the CO2 underground in old oil or gas wells, coal mines, or porous rocks filled with salt water. Global estimates are that 11,000 billion tonnes of CO2 could be disposed of underground, several times more than the likely emissions of CO2 from burning fossil fuels in the coming century. This could give the world extra time to give up its reliance on fossil fuels. The following bar chart shows the distribution of space available to bury CO2 gas underground. a. Explain why the break is found in the third bar. b. Why was the graph constructed with a broken bar?
Assume that you can contribute $7,000 per year into a retirement fund that grows at a constant rate of 7% per year. (a) Write a first-order linear differential equation that models your retirement savings. (b) find the total amount saved after 10 years. (c) assume that instead of contributing $7,000 per year, you were able to increase your contribution by $50 each year ($7,000 first year, $7,050 second year, etc.). How much money would you have saved after 10 years?
A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: People (P) 10 10 9 7 8 5 4 4 Cups of coffee (n) 1 1 2 3 3 4 5 5 Unless otherwise stated, you can round values to two decimal places.a) Using regression to find a linear equation for P(n)P(n) = b) Interpret the meaning of the slope of your formula in the context of the problemc) Interpret the meaning of the P intercept in the context of the problemd) Use your model to predict the number of people that will complain about his attitude if he drinks 8 cups of coffee.(Round to 2 decimals) e) Is the answer to part d reasonable? Why or why not?f) How many cups of coffee should he drink so that no one will complain about his attitude? It is ok to round to one decimal place.
Read the section "Sections 1.1-1.3:" and respond the following questions. 1. Classify each equation as ordinary differential equation (ODE) or as partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear. a. b. d. e. du du ox² + =0 d³m m(5+6n) dn n(2–4m) 4y" + xy' = 6y³ ry"+cosx(y) =rẻ

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