The number of milligrams, $d$, of a drug remaining in a patient's bloodstream, $t$ hours after it has been administered, is given by the equation $d = 5(2.7^{.04t})$. To the nearest minute, how long will it take until only $2.5$ mg of the drug remains in the system?
First, I set the equation equal to 2.5 and solved for $t$, where $t=1.7$. However, I am way off from my teacher's answer which was 31 hours and 45 minutes. I'm uncertain of another way to solve the problem. What else do I need to do?
d = 5*(2.7^.04t) //(original equation) 2.5 = 5*(2.7^.04t) //(set equation equal to 2.5) 0.5 = 2.7^.04t //(divide by 5 on both sides) log base 2.7 of 0.5 = 0.04t //(log function) t = 17.446241... //(Answer)
You should probably talk to your teacher and ask her how he/she did the question.