The formula D 50 e05h can be used to find the number of mil

The formula D = 50 e^-0.5h can be used to find the number of milligram D of a certain drug that is in a patient\'s bloodstream h hours after the drug was administered. When the number of milligram reaches 4, the drug is to be administered again. What is the time between injection? The time between injection is hours(s). (Type an integer or a decimal rounded to two decimal places as needed.)

Solution

D = 50 e^-0.5h

When the number of milligrams reaches 4, the drug has to be administered again. This means:

D = 4 milligrams

This value of D , we will put in above equation to find h which is the time between the injections.

4 = 50 e^-0.5h

4/50 = e^-0.5h

0.08 = e^-0.5h

Take ln on the both the sides, we get:

ln 0.08 = ln e^-0.5h

-2.5257 = -0.5h (ln e)

2.5257 = 0.5 h (1)

h = 2.5257/ 0.5

h = 5.0514

h = 5.05 hours

Therefore, time between injections is of 5.05 hours