Respuesta :
The exponential function that represents the amount of acetaminophen in the patient's bloodstream t hours after the medicine is administered is given by:
[tex]P(t) = 800e^{-0.23104906t}[/tex]
Using this function, it is found that 1217.5 mg will be in the patient's bloodstream if the patient is given a second dose of 800 mg four hours after the first dose.
What is an exponential function?
It is modeled by:
[tex]P(t) = P(0)e^{-kt}[/tex]
In which:
- P(0) is the initial value.
- k is the decay rate, as a decimal.
In this problem, the half-life is of 3 hours, hence:
P(3) = 0.5P(0)
[tex]0.5P(0) = P(0)e^{-3k}[/tex]
[tex]e^{-3k} = 0.5[/tex]
[tex]\ln{e^{-3k}} = \ln{0.5}[/tex]
[tex]-3k = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{3}[/tex]
k = 0.23104906.
Considering the initial amount of P(0) = 800, the equation is:
[tex]P(t) = 800e^{-0.23104906t}[/tex]
After 4 hours, the amount is:
[tex]P(4) = 800e^{-0.23104906 \times 4} = 317.5[/tex]
Considering the second dose of 800 mg, 800 + 317.5 = 1217.5 mg will be in the patient's bloodstream if the patient is given a second dose of 800 mg four hours after the first dose.
More can be learned about exponential functions at https://brainly.com/question/25537936
