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The actual half-life of amoxicillin is about 62 minutes. Recall that half-life is the amount of time it takes for a substance to decay to half of its original amount. How long after Haidar gives Aldi his last dose of medication will it take before the amount of medication in Aldi's bloodstream is effectively 0? Describe how you determined your solving method.

Sagot :

Using an exponential function, it would take 824 minutes before the amount of medication in Aldi's bloodstream is effectively 0.

How to determine the time

A decaying exponential function is given as;

[tex]A(t) = A(0)e^-kt[/tex]

Where A = initial value

k = decay constant

We have the half-life of amoxicillin as 62minutes, to determine k, we get

[tex]A(62) = 0. 5(0)[/tex]

[tex]A(62) = 0.5A(0)[/tex]

[tex]0. 5A(0) = A(0) e^{-62k}[/tex]

Solve the exponential function thus

[tex]e^{-62k} = 0. 5[/tex]

㏑ [tex]e^{-62k}[/tex] = ㏑ 0. 5

- 62k = ㏑ 0.5

Make k subject of formula

k = -㏑[tex]\frac{0. 5}{62}[/tex]

k = 0. 011179

The equation is given by

[tex]A(t) = A(0)e^-0.011179[/tex]

We have

[tex]0. 0001A(0) = A(0)e^-0.01179[/tex]

[tex]e^-0.011179t = 0. 0001[/tex]

㏑ [tex]e^-0.011179[/tex] = ㏑ 0.0001

[tex]-0.011179t = In 0.0001[/tex]

t = [tex]-\frac{In 0. 0001}{0. 011179}[/tex]

t = [tex]824[/tex]

Therefore, it would take 824 minutes before the amount of medication in Aldi's bloodstream is effectively 0.

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