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?

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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**

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