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A patient has swallowed some medication. The amount of the medication n the bloodstream...
A patient has swallowed some medication. The amount of the medication n the bloodstream in mm is given by the function f(t)=6te^(0.05t^2)
where t is the time in hours since its swallowed. what is the average amount of medication in the bloodstream in mm between 6 and 10 hours after swallowing
1 Answer | add yours
High School Teacher
Since you are given a function and the interval, you can use the formula:
`f(x) = f(t) = 6t e^(0.05t^(2))`
b = 10
a = 6
Plug in the given in the formula:
You can move out 6 so it will look like this:
`f_(ave) = (6)int_6^10(e^(0.05t^(2)))tdt`
To get the integral of `te^(0.05t^(2))`
you can use substitution method, where `e^(0.05t^(2))`
is in the form `e^(u)`
so u = `0.05t^(2)`
Get the derivative of u, so du = 2 * (0.05) t = 0.1t dt.
From that you can get `tdt = (du)/(0.1)`
The integral of `e^(u) du = e^(u)`
so `(6) int (e^(u)/(.01)) du = 60 e^(u)`
Now plug-in `0.05t^(2)`
in place of u then evaluate from 6 to 10.
`60 e^(0.05(10)^(2)) - 60 e^(0.05(6)^(2)) = 8541.8106 mm`
`f_(ave) = 1/(10-6)int_6^10(6te^(0.05t^2))`
`f_(ave) = 1/4 * (8541.8106)`
`f_(ave) = 2135.45265`
``The answer is `2135.45265 mm.`
Posted by mariloucortez on March 12, 2013 at 12:45 PM (Answer #1)
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