Homework Help

Insulin is a polypeptide hormone released from the pancreas that stimulates fat and...

user profile pic

kathyyyyyy123 | Student, Undergraduate | (Level 1) Honors

Posted July 13, 2013 at 4:59 AM via web

dislike 1 like

Insulin is a polypeptide hormone released from the pancreas that stimulates fat and muscle to take up glucose. In a certain patient, it has a first order half-life in the blood of 3.5 min. To maintain an adequate blood concentration of insulin, it must be replenished in a time interval equal to 1/k. How long is the time interval in this patient?

 

1 Answer | Add Yours

user profile pic

jerichorayel | College Teacher | (Level 1) Senior Educator

Posted July 13, 2013 at 6:49 AM (Answer #1)

dislike 1 like

The half-life for the first order reaction of insulin in the body is expressed as:

 

`t_(1/2) = ln(2)/k `

Where:

`t_(1/2) ` = 3.5 minutes

`k` = rate constant

We should first solve for the rate constant:

 

`t_(1/2) = (ln 2)/(k) `

 

`k = (ln 2)/(t_(1/2)) `

 

`k = (ln 2)/(3.5 min) `

 

`k = 0.19804 min^(-1) `

 

For the time interval, it says that it must be replenished in a time interval equal to `1/k` , therefore:

Time interval `= 1/k = 1/(0.19804 min^(-1))`

Time interval = 5.049 min = 5.0 minutes -> answer

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes