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Sagot :
When people take medicine, the drug gets metabolized by the body and eliminated at a constant rate.
Suppose the initial amount of a drug in the body is 549 mg and it is eliminated at a rate of 12% per hour.
Let f(x) refer to the amount of drug left in the body after I hours.
(a) Write down an exponential function to model this situation. Write your answer using function
notation
(b) How much of the drug is left in the body after 12 hours? Round to the nearest whole number.
(c) How much of the drug is left in the body after 180 minutes? Round to the nearest whole number
Part a)
Let
t -----> number of hours
f(x)=a(1+r)^t
where
a=549 mg
r=12%=0.12
substitute
f(x)=549(1+0.12)^t
f(x)=549(1.12)^t
Part b)
For t=12 hours
substitute in the function
f(12)=549(1.12)^12
f(12)=2,139 mg
Part c)
For t=180 minutes
Remember that
1 h=60 minutes
so
180 minutes=180/60=3 hours
For t=3 hours
substitute
f(3)=549(1.12)^3
f(3)=771 mg
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