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3. 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 functionnotation(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

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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