Newtons Method (1 Viewer)

[fashionista]

heeeeey!! i have a question i am desperate to get answered..i've tried soo many times but i keep gettin the wrong answer oh so slightly..i think it's my differentiating again but anyway here it is:
After an injection the concentration, c(t), of a certain drug in the patient's blood is given by c(t)=te^(-t/2) where t is the time measured in hours. the next injection is given when c(t) falls to 0.05. It is estimated that it is about 10.7 hours. Use one application of Newton's method to find an improved estimate.
Please answer this for me so i can prove the book is wrong!!!!

 

[fashionista]

PLEEEEEEEEAAAASSSEEE SOME ONE HELP ME!!!!!!!!

 

[acmilan]

i get 10.739 to 3dp but i havnt written anything just did it in my head and calculator so it might not be right

 

[fashionista]

garrrr!! thats the answer!! tell me how!!


.....Please

 

[acmilan]

Originally posted by fashionista
heeeeey!! i have a question i am desperate to get answered..i've tried soo many times but i keep gettin the wrong answer oh so slightly..i think it's my differentiating again but anyway here it is:
After an injection the concentration, c(t), of a certain drug in the patient's blood is given by c(t)=te^(-t/2) where t is the time measured in hours. the next injection is given when c(t) falls to 0.05. It is estimated that it is about 10.7 hours. Use one application of Newton's method to find an improved estimate.
Please answer this for me so i can prove the book is wrong!!!!

you are looking for time that c(t) falls to 0.05 so:

te^(-t/2) = 0.05

te^(-t/2) - 0.05 = 0

call this f(t) = te^(-t/2) and find f'(t) and then sub in 10.7 into f(t) and f'(t) and then use newtons method

t(2) = t(1) - [f(t)/f'(t)] (where t(1) = 10.7)