Respuesta :
Answer:
At x = 0, Sensitivity = Not defined
At x = 1, Sensitivity = 3.2974
At x = 2, Sensitivity = 2.71825
At x = 5, Sensitivity = 4.8729
At x = 10, Sensitivity = 29.6826
Step-by-step explanation:
We are given the following in the question:
[tex]y = 2e^{0.5x}[/tex]
where y is the output and x is the input of a system.
We define sensitivity as the ration of output to input.
[tex]\text{Sensitivity} = \displaystyle\frac{\text{Out-put}}{\text{In-put}} = \frac{y}{x}[/tex]
At x = 0
[tex]y = 2e^{0.5(0)} = 2\\\\\text{Senstivity} = \displaystyle\frac{2}{0} = \text{N.D}[/tex]
At x = 1
[tex]y = 2e^{0.5(1)} =3.2974\\\\\text{Senstivity} = \displaystyle\frac{3.2974}{1} = 3.2974[/tex]
At x = 2
[tex]y = 2e^{0.5(2)} =5.4365\\\\\text{Senstivity} = \displaystyle\frac{5.4365}{2} = 2.71825[/tex]
At x = 5
[tex]y = 2e^{0.5(5)} =24.3649\\\\\text{Senstivity} = \displaystyle\frac{24.3649}{5} = 4.8729[/tex]
At x = 10
[tex]y = 2e^{0.5(10)} =296.8263\\\\\text{Senstivity} = \displaystyle\frac{296.8263}{10} = 29.6826[/tex]
