Respuesta :
Answer:
amount of the drug becomes approximately equal to 0.2 milligrams after 13.04 hours
Step-by-step explanation:
Given: The function [tex]f(t)=10e^{-0.3 t}[/tex] 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:
[tex]f(t)=10e^{-0.3 t}\\0.2=10e^{-0.3 t}\\\frac{0.2}{10}=e^{-0.3 t}\\\frac{2}{100}=e^{-0.3 t}\\\frac{1}{50}=e^{-0.3 t}\\[/tex]
As [tex]e^x=y\Rightarrow x=\ln y[/tex] ,
[tex]50=e^{0.3 t}\\0.3t=\ln 50\\t=\frac{\ln 50}{0.3}=13.04\,\,hours[/tex]
So, amount of the drug becomes approximately equal to 0.2 milligrams after 13.04 hours
