The 17.42 mg will be left after 12 hours if Sarah takes 550 mg of an antibiotic. Every hour, her body breaks down 25% of the remaining drug.
It is given that the equation to model Exponential Decay is:
[tex]\rm y=a(1-r)^t[/tex] ,
Where y = total amount,
a = starting amount
r = the growth rate/exponential decay rate as a decimal
t = number of growth periods
It is required to find how much antibiotic will be left after 12 hours if Sarah takes 550 mg of an antibiotic. Every hour, her body breaks down 25% of the remaining drug.
It is defined as decreasing an amount by a definite percentage over the span of a time, the original amount decay exponentially.
We have a = 550 mg
r = 25% = 0.25
t = 12 hours
Putting these values in the Exponential Decay equation, we get:
[tex]\rm y=550(1-0.25)^1^2\\\\\rm y = 550(0.75)^1^2\\\\\rm y =550(0.03167)\\\\\rm y = 17.42 mg[/tex]
Thus, the 17.42 mg will be left after 12 hours if Sarah takes 550 mg of an antibiotic. Every hour, her body breaks down 25% of the remaining drug.
Learn more about Exponential Decay here:
https://brainly.com/question/2193820
The 17.42 mg will be left after 12 hours if Sarah takes 550 mg of an antibiotic. Every hour, her body breaks down 25% of the remaining drug.
The equation to model exponential decay is
[tex]y=a(1-r)^t[/tex]
Where y = total amount,
a = starting amount
r = the growth rate/exponential decay rate as a decimal
t = number of growth periods
It is required to find how much antibiotic will be left after 12 hours if Sarah takes 550 mg of an antibiotic. Every hour, her body breaks down 25% of the remaining drug.
The exponential decay defined as decreasing an amount by a definite percentage over the span of a time, the original amount decay exponentially.
We have given that a = 550 mg
r = 25%=25/100 = 0.25
t = 12 hours
plug these values in the exponential decay equation,
[tex]y=550(1-0.25)^12\\y=550(0.75)^12\\y=550(0.03167)\\y=17.42mg[/tex]
Therefore, the 17.42 mg will be left after 12 hours if Sarah takes 550 mg of an antibiotic. Every hour, her body breaks down 25% of the remaining drug.
To learn more about the exponential deacy visit:
https://brainly.com/question/2046253
