Arithmetic and Geometric Sequences in Hospital Drug Dosage Calculations

let's go to 4a on her first day in hospital kiri receives the usable one milligram

of a drug the

amount of the drug kiri receives increases by the same amount d each day

this shows is an arithmetic sequence on the seventh day she

received 21. on seventh day she receives

21 milligram of the drug on the 11th day she receives 29

milligrams write down an equivalent in terms of usable 1 and a d

for the amount of drug she receives on the 7th state we know this is a arithmetic sequence so

usable n equals u sub 1 plus n minus 1 times d so for u sub 7 equals u sub 1 plus 6 d

for b write down an equation in terms of usable 1 and a d for the amount of drug that she receives on the 11th state

use of 11 equals usable 1 plus 10d let's go to 4c write down the value of d and

value of u 1. we got these two equations u sub 11.

equals u sub 1 plus 10 d u sub 7 equals u sub 1 plus 6 d this is the first equivalent second

equivalent we will do subtraction get u sub 11 minus u sub 7 cancel these two

equals 10 d minus 16 will be 4 d then we plug in numbers u sub 11 is a 29 minus u sub 7 is 21 equals 4 d

8 equals 4 d so d equals 2

then we plug back to u sub 7 equals u sub 1 plus

60 u sub 7 is a 21 equals u sub 1 plus 6 times 2 is a 12.

so u sub 1 equals 21 minus 12 will be 9. for 4d

kiri receives the drug for 30 days calculate the total amount total amount which means the

s sub 30. we will use this formula 30 over 2 times 2

times the u sub 1 is 9 plus n minus 1 is 29 times a

2 then we put it into calculator enter

answer will be 1140 1140 milligrams

will be the solution to 4d let's go to 4e ted is also in a hospital and on his first date he receives a 20

milligram injection the amount of

ted receives decreased the by 40

each day by 40 percent each day which means this is a

geometrical sequence r equals 1 minus 40 percent that equals 0.6 find the amount of for

antibiotic in milligram that ted receives on the fifth day

we know this is a geometrical sequence so u sub

5 equals u sub 1 times r to the fourth power u sub 1 is 20

r is 0.6 to the fourth power we will get 2.592

milligrams for 4f the daily amount of for antibiotics had

received will first be less than 0.06 milligram on the key date from the key we know the use of a k

less than 0.06 usable k we do know this is a geometrical sequence usable n equals

u sub 1 times r to the n minus 1 power now we plug in u sub 1 is 20 r is 0.6

to the k minus 1 power

less than 0.06 we will use the ukraine solver to figure

out the solution get less than

zero form first move 0.06 to the left side 20 times 0.6

to the k minus 1 power minus 0.06 go to calculator 20 times the 0.6

to the x minus the ones power then minus 0.06 math

upper arrow solver 10 as an estimated value alpha enter

answer will be 12.4 by solver k equals 12.4

two choices either k equals 12 or k equals 13. we plug back into this

you know quality 13 we will get a negative number

but if you put in 12 you will get positive number

but we are looking for the solution to make

less than zero inequality so k equals 13 will be the solution

for 4g hence find the total amount of anti-biotic

in milligram that teddy receives during the first k days we are looking for s is about k

we already know k is a 13. so basically we are looking for x is about 13 using this

formula 20 times 0.6

to the 13th power minus 1 0.6 minus 1

go to alpha y equals get a fraction 20 times

0.6 to the 13th power -1

0.6 minus 1 enter answer will be 49.9

milligram so answer to 4g will be 49.9 milligrams [Music]

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