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Social ScienceThe number of miligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled byx(t)= 2000t/t^2+16(a) For what t-values is x increasing?(b) Find the t-value at which s is maximum.(c) Fine the maximum value of x.
The number of miligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by
x(t)= 2000t/t^2+16
(a) For what t-values is x increasing?
(b) Find the t-value at which s is maximum.
(c) Fine the maximum value of x.
Expert Answer
we are given a function
Image Transcriptionclose
2000t x(t) t16
Now, we will find derivative and then we can set derivative to 0
and then we can solve for t
and then we find point and time can never be negative
so, we will only consider t=4
Image Transcriptionclose
2000 dr t16 x'(t) 2000 dtt16 d 0(F+16) ( +16)t dt -2000. dt (P+16) 2000. 1-(16)-2ft (+16) 2000 (-r16) x'(t (P+16) 2000(-16) (r+16) t-4,t 4 x(4) =2000(4) 42+16 x(4) 250
Now, we can draw a number line and locate t=4
and then we can find sign of derivative on each intervals
Image Transcriptionclose
+ 4
Math
Calculus
Derivative
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