Only question 5 5. Previously we used the recurrence relation dn+1 = 0.5dn + 200, di = 200 and the assumptionthat d, L to compute the limiting value. Compute L is this way and compare to your%3Danswer in 4. Let us revisit a question from a few problem sets ago with slightly different numbers. A patienttakes 200 mg of an antibiotic every 6 hours. The half-life of the drug (the time it takes for halfof the drug to be eliminated from the blood) is 6 hours. Let dn denote the amount (in mg) ofmedication in the bloodstream after n doses, where dı = 200.1. Explain why dn+1 = 0.5dn + 200, d1 = 200 is the correct recurrence relation.

Given dn+1=0.5dn+200 and dn→L as n→∞. To find L .

Answered: 5. Previously we used the recurrence…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Determinants

Section3.CM: Cumulative Review

Problem 17CM: Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]

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13. Solve the recurrence relation. Given:a0=3 a1= 6 an= 6a n-1 + 7a n-2 Show your work in the space provided. a. Find c1 and c2 an= (6)a n-1 + (7)a n-2 c1= c2= b. Substitute c1 and c2 into the following equation: r^2- c1r - c2= 0 show your work here: c. Identify a, b, and c in the quadratic equation. a= b= c= d. Use the quadratic formula to find the two roots. Here is the quadratic formula: -b + Vb^2- 4ac/2a Show your work here: e. Substitute two roots, r1 and r2 into the equation an= a1r1^n+ a2r2^n Show your work here: f. Now substitute to find two equations, a0 and a1 Remember to use the equation you found from step e. show your work here: a0= 3 =a1= 6 = g. Add the two equations together find a1 and a2 a1= a2= h. What is the solution to the recurrence relations? an= i. Find the 10" term of the sequence, using the solution to the recurrence relation you just found. Show your work here: a10=

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5. Previously we used the recurrence relation dn+1 = 0.5dn + 200, d₁= 200 and the assumption that dnL to compute the limiting value. Compute L is this way and compare to your answer in 4.