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Application - Medicine The concentration, in micrograms per milliliter, of a particular medication in the bloodstream ₺ hours after intravenous administration can be modeled using the function C'(t) 3+² 1+.15³ What is the instantaneous rate of decline of the concentration at t = 6 hours? Guiding Discussion Questions: • How do you choose what computations to do to find this? • What differentiation rules will help here? Find the tangent line to the graph of C(t) at t = 6, showing all the steps in your process.

Application - Medicine The concentration, in micrograms per milliliter, of a particular medication in the bloodstream ₺ hours after intravenous administration can be modeled using the function C'(t) 3+² 1+.15³ What is the instantaneous rate of decline of the concentration at t = 6 hours? Guiding Discussion Questions: • How do you choose what computations to do to find this? • What differentiation rules will help here? Find the tangent line to the graph of C(t) at t = 6, showing all the steps in your process.

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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The first three subparts were already answered. So I need the rest of it pls and thanks!

Application - Medicine The concentration, in micrograms per milliliter, of a particular medication in the bloodstream ₺ hours after intravenous administration can be modeled using the function C'(t) : = 3t² 1+.15t³ What is the instantaneous rate of decline of the concentration at t - 6 hours? Guiding Discussion Questions: • How do you choose what computations to do to find this? • What differentiation rules will help here? Find the tangent line to the graph of C(t) at t = 6, showing all the steps in your process. Guiding Discussion Questions: • What steps do we need to follow to find a tangent line? Graph both C(t) and the tangent line you found using technology. Guiding Discussion Questions: • How can you use the graph to determine if the equation for the tangent line you found is correct? Suppose the dosage is given at 1:00pm. Use the tangent line at ₺ = 6 to estimate the concentration of the medication in the bloodstream at 7:30pm. What is the error on this estimate? (In other words, how far off is the estimate from the actual value?) Guiding Discussion Questions: • How do we use tangent lines to estimate function values? What examples have we seen of this process so far? • What time does t = 0 correspond to? Why? • What time does t = 6 correspond to? • What t value does 7:30pm correspond to? • How does keeping track of what times correspond in our function, help us choose computations to do?
Transcribed Image Text:Application - Medicine The concentration, in micrograms per milliliter, of a particular medication in the bloodstream ₺ hours after intravenous administration can be modeled using the function C'(t) : = 3t² 1+.15t³ What is the instantaneous rate of decline of the concentration at t - 6 hours? Guiding Discussion Questions: • How do you choose what computations to do to find this? • What differentiation rules will help here? Find the tangent line to the graph of C(t) at t = 6, showing all the steps in your process. Guiding Discussion Questions: • What steps do we need to follow to find a tangent line? Graph both C(t) and the tangent line you found using technology. Guiding Discussion Questions: • How can you use the graph to determine if the equation for the tangent line you found is correct? Suppose the dosage is given at 1:00pm. Use the tangent line at ₺ = 6 to estimate the concentration of the medication in the bloodstream at 7:30pm. What is the error on this estimate? (In other words, how far off is the estimate from the actual value?) Guiding Discussion Questions: • How do we use tangent lines to estimate function values? What examples have we seen of this process so far? • What time does t = 0 correspond to? Why? • What time does t = 6 correspond to? • What t value does 7:30pm correspond to? • How does keeping track of what times correspond in our function, help us choose computations to do?
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