Find an equation and use it to find the level of the drug in the blood six hours after it is taken?

Question

1 tablet of medication contains 5.0 milligrams (mg) of phenylephrine.

The table below shows the decay of this drug in the blood over a period of four hours after it is taken

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Answer 1 · 2018-08-03T10:00:52

#1.31mg#

#A=A_0e^(-kt)#
Where
#A_0# is the initial level of phenylephrine
#A# is the current level of phenylephrine
#t# is the time

The #k# is negative because it is an exponential decay

Looking at the table, we can tell #A_0=5#

To find #k#, we know that #t=1#, #A=4#

#4=5e^(-k)#

#4/5=e^(-k)#

#In(4/5)=-k#

#k=-In(4/5)#

#A=5e^((In4/5)t#

When #t=6#,

#A=5e^((In4/5)times6#

#A=1.31#