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Sagot :
Using an exponential function, it is found that it will take 19.76 hours for there to be only 8% of the original amount in the patient's bloodstream.
What is an exponential function?
A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
For this problem, the decay rate is of 12%, hence:
r = 0.12.
And the equation is:
[tex]A(t) = A(0)(0.88)^t[/tex]
8% of the original amount will be in the patient's bloodstream after t hours, for which A(t) = 0.08A(0), hence:
[tex]A(t) = A(0)(0.88)^t[/tex]
[tex]0.08A(0) = A(0)(0.88)^t[/tex]
[tex](0.88)^t = 0.08[/tex]
[tex]\log{(0.88)^t} = \log{0.08}[/tex]
[tex]t\log{0.88} = \log{0.08}[/tex]
[tex]t = \frac{\log{0.08}}{\log{0.88}}[/tex]
t = 19.76 hours.
It will take 19.76 hours for there to be only 8% of the original amount in the patient's bloodstream.
More can be learned about exponential functions at https://brainly.com/question/25537936
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