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The number of milligrams of a drug in a person’s body after t hours is given by the function f(t) = 10e-0.3t. When will the amount of the drug be approximately 0.2 milligrams?

2 Answers

4 votes

Answer:

13 hours

Explanation:

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User Hans Wassink
by
7.8k points
0 votes

Answer:

amount of the drug becomes approximately equal to 0.2 milligrams after 13.04 hours

Explanation:

Given: The function
f(t)=10e^(-0.3 t) represents number of milligrams of a drug in a person’s body after t hours

To find: time after which amount of the drug becomes approximately 0.2 milligrams

Solution:


f(t)=10e^(-0.3 t)\\0.2=10e^(-0.3 t)\\(0.2)/(10)=e^(-0.3 t)\\(2)/(100)=e^(-0.3 t)\\(1)/(50)=e^(-0.3 t)\\

As
e^x=y\Rightarrow x=\ln y ,


50=e^(0.3 t)\\0.3t=\ln 50\\t=(\ln 50)/(0.3)=13.04\,\,hours

So, amount of the drug becomes approximately equal to 0.2 milligrams after 13.04 hours

User Mahesh Keshvala
by
8.8k points
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