Respuesta :
The times(t) corresponding to the inflection points is 100, 300.
Consider the function S(t)=[tex]\mathrm{At}^{\mathrm{P}} \mathrm{e}^{-\mathrm{kt}}$[/tex]
Where A=0.3, p=4, k=0.02
[tex]$\mathrm{S}(\mathrm{t})=0.03 \mathrm{t}^4 \mathrm{e}^{-0.02 \mathrm{t}}$[/tex]
Find first derivative of the function using product rule.
[tex]\begin{array}{rc}S^{\prime \prime}(t)=\end[/tex][tex]\\& \frac{d}{d t}\left(t^3 e^{-0.02 t}(0.12-0.0006 t)\right) \\[/tex]
[tex]= & \frac{d}{d t}\left(t^3\right) e^{-0.02 t}(0.12-0.0006 t)+\frac{d}{d t}\left(e^{-0.02 t}(0.12-0.0006 t)\right) t^3 \\[/tex]
[tex]= & 3 t^2 e^{-0.02 t}(0.12-0.0006 t)+\left(0.000012 e^{-0.02 t} t-0.003 e^{-0.02 t}\right) t^3 \\[/tex]
[tex]= & e^{-0.02 t} t^2\left(3(0.12-0.0006 t)+0.000012 t^2-0.003 t\right) \\[/tex]
[tex]= & e^{-0.02 t} t^2\left(0.000012 t^2-0.0048 t+0.36\right)\end{array}$[/tex]
Now to find inflection points, set [tex]f^{''} (x)=0[/tex] then solve f(x)=0
The point of inflection defines the slope of a graph of a function in which the particular point is zero. It shows the function has an inflection point.
It is noted that in a single curve or within the given interval of a function, there can be more than one point of inflection.
[tex]\begin{aligned}& \mathrm{e}^{-0.02 \mathrm{t}} \mathrm{t}^2\left(0.000012 \mathrm{t}^2-0.0048 \mathrm{t}+0.36\right)=0 \\& 0.000012 \mathrm{t}^2-0.0048 \mathrm{t}+0.36=0 \\& 0.000012\left(\mathrm{t}^2-400 \mathrm{t}+30,000\right)=0 \\& 0.000012(\mathrm{t}-300)(\mathrm{t}-100)=0 \\& \mathrm{t}=100,300\end{aligned}$[/tex]
Therefore, the time is 100,300
For such more questions about inflection points
https://brainly.com/question/29017999
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Question is incomplete:-
A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function
S(t) = Atpe−kt
A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function
S(t) = Atpe−kt (where t > 0) is often used to model the response curve, reflecting an initial surge in the drug level and then a more gradual decline. If, for a particular drug, A = 0.03, p = 4, k = 0.02, and t is measured in minutes, estimate the times t corresponding to the inflection points. (Round your answers to two decimal places.)
