Logarithms

Case

Application of Logarithms• Calculating frequency at which a patient

needs to take a dose of this drug

m=Ae-kt

Amount of medicine left in body constants

Time since last dosage

Calculator value of e

Application of Logarithms

• Equation converted to logarithmic form

lnm = -kt + lnA

In the form of y=mx+c

Can plot graph

Data

t (hours) m (mg)

0 200

2 127

4 79

6 50

10 20

30mg<m<300mg

Questions

• There shouldnot be more than 300mg of the drug in the body, beyond which the drug becomes toxic. Is it advisable to take another dose after 2.5 hours? (assuming 1 dosage is 200mg)

NO, amount of medicine left +200-> more than 300mg

m=Ae-kt

A = 200K = 0.227

Questions

• Estimate amount of drug left in patient’s body after 8 hours

m=Ae-kt

A = 200K = 0.227

Ans:32.5mg

Conclusion

1 dosage to be taken every 6 hours, if not you’ll die of drug overdose

•Thanks