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a) What type of model function is suggested by the observation "as the iodine concentration in the gland increases, it becomes harder and harder to add more iodine"? b) Suppose we knew the normal iodine concentration Io in the thyroid gland and we knew the maximum concentration Imax that the thyroid could possible hold. Explain the model formula below, where 7 is the elapsed time since the nuclear accident and we haven't done any experiments to determine B. I(T) = (lo - Imax) e-BT + Imax In particular you should explain both the appearance of Imax as the +C term and why the A term in the model needs to be lo - Imax.

a) What type of model function is suggested by the observation "as the iodine concentration in the gland increases, it becomes harder and harder to add more iodine"? b) Suppose we knew the normal iodine concentration Io in the thyroid gland and we knew the maximum concentration Imax that the thyroid could possible hold. Explain the model formula below, where 7 is the elapsed time since the nuclear accident and we haven't done any experiments to determine B. I(T) = (lo - Imax) e-BT + Imax In particular you should explain both the appearance of Imax as the +C term and why the A term in the model needs to be lo - Imax.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Hi please do not reject this question even if you can only do and b that would be so helpful thank you!!

Section 1.57251, 253, 260, 272, 275, 2 288, 291, 300 (you may use e ≈ 2.71828 instead of 2.7 for the base of the exponential), 304, 307 Here's an interesting extension of 304. You may be following the invasion of Ukraine by Russia and the concerns over the Zaporizhzhia nuclear power plant (ZNPP). Within the last week or so, the government of Ukraine began dispensing iodine tablets to residents near the plant. The explanation for this follows: It turns out the the thyroid gland is the repository for iodine in your body, so radioactive iodine that would be released from ZNPP in the event of a catastrophe would tend to become concentrated in the thyroid. Iodine tablets help because as the iodine concentration in the gland increases, it becomes harder and harder to add more iodine. YOUR PROBLEM A: a) What type of model function is suggested by the observation "as the iodine concentration in the gland increases, it becomes harder and harder to add more iodine"? b) Suppose we knew the normal iodine concentration Io in the thyroid gland and we knew the maximum concentration Imax that the thyroid could possible hold. Explain the model formula below, where is the elapsed time since the nuclear accident and we haven't done any experiments to determine B. - Imax) e-BT + Imax In particular you should explain both the appearance of Imax as the +C term and why the A term in the model needs to be Io - Imax. I(T) = c) Provide a sketch showing the general shape of the graph in (1). Label the features of the graph that depend on Io and Imax, then describe any effect that increasing or decreasing B would have (either in words or on a separate graph). I(x) d) We haven't thought about the chemical mechanism involved. The model in part b) works if the primary gateway for iodine into the cells is via diffusion through the cell membrane. An alternative would be for the iodine to bind to a receptor. It's a good thing we studied Hill functions. Make the same sort of explanation as in part b) for the model formula xn K+xn Here x is iodine concentration in the blood, not time, and again we have not done any experiments that would allow us to estimate n and K. e) Here's a plot the function in (2) using K = 1 and n = 2 (blue) and n = 5 (gold). = 1.0 (10 % Iodine saturation 0.8 0.6 0.4 (Imax - 10) 1 2 + Io 3 4 5 6 7 conc in blood n=2 n=5 (1) f) Suppose the chemistry suggests that K = 1, n = 5 is correct. How could you determine which model (cell membrane or chemical binding) is best based on a graph of actual Iodine in the thyroid of your patient? In other words, compare and contrast your sketch in from part c) with the n = 5 plot in part e). Your goal is to tell me what to look for in the graph of the data in order to make a snap judgement as to which model is best. YOUR PROBLEM B: (2)
Transcribed Image Text:Section 1.57251, 253, 260, 272, 275, 2 288, 291, 300 (you may use e ≈ 2.71828 instead of 2.7 for the base of the exponential), 304, 307 Here's an interesting extension of 304. You may be following the invasion of Ukraine by Russia and the concerns over the Zaporizhzhia nuclear power plant (ZNPP). Within the last week or so, the government of Ukraine began dispensing iodine tablets to residents near the plant. The explanation for this follows: It turns out the the thyroid gland is the repository for iodine in your body, so radioactive iodine that would be released from ZNPP in the event of a catastrophe would tend to become concentrated in the thyroid. Iodine tablets help because as the iodine concentration in the gland increases, it becomes harder and harder to add more iodine. YOUR PROBLEM A: a) What type of model function is suggested by the observation "as the iodine concentration in the gland increases, it becomes harder and harder to add more iodine"? b) Suppose we knew the normal iodine concentration Io in the thyroid gland and we knew the maximum concentration Imax that the thyroid could possible hold. Explain the model formula below, where is the elapsed time since the nuclear accident and we haven't done any experiments to determine B. - Imax) e-BT + Imax In particular you should explain both the appearance of Imax as the +C term and why the A term in the model needs to be Io - Imax. I(T) = c) Provide a sketch showing the general shape of the graph in (1). Label the features of the graph that depend on Io and Imax, then describe any effect that increasing or decreasing B would have (either in words or on a separate graph). I(x) d) We haven't thought about the chemical mechanism involved. The model in part b) works if the primary gateway for iodine into the cells is via diffusion through the cell membrane. An alternative would be for the iodine to bind to a receptor. It's a good thing we studied Hill functions. Make the same sort of explanation as in part b) for the model formula xn K+xn Here x is iodine concentration in the blood, not time, and again we have not done any experiments that would allow us to estimate n and K. e) Here's a plot the function in (2) using K = 1 and n = 2 (blue) and n = 5 (gold). = 1.0 (10 % Iodine saturation 0.8 0.6 0.4 (Imax - 10) 1 2 + Io 3 4 5 6 7 conc in blood n=2 n=5 (1) f) Suppose the chemistry suggests that K = 1, n = 5 is correct. How could you determine which model (cell membrane or chemical binding) is best based on a graph of actual Iodine in the thyroid of your patient? In other words, compare and contrast your sketch in from part c) with the n = 5 plot in part e). Your goal is to tell me what to look for in the graph of the data in order to make a snap judgement as to which model is best. YOUR PROBLEM B: (2)
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