Question

Let x and y be the input and output of a measurement system, respectively. It is known that their relationship is 2 0.5 x =  . (a) Calculate the sensitivity of this measurement, when x = 0, 1, 2, 5, and 10.

Answer 1

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

Explanation:

We are given the following in the question:

`y = 2e^(0.5x)`

where y is the output and x is the input of a system.

We define sensitivity as the ration of output to input.

`\text{Sensitivity} = \displaystyle\frac{\text{Out-put}}{\text{In-put}} = (y)/(x)`

At x = 0

`y = 2e^(0.5(0)) = 2\\\\\text{Senstivity} = \displaystyle(2)/(0) = \text{N.D}`

At x = 1

`y = 2e^(0.5(1)) =3.2974\\\\\text{Senstivity} = \displaystyle(3.2974)/(1) = 3.2974`

At x = 2

`y = 2e^(0.5(2)) =5.4365\\\\\text{Senstivity} = \displaystyle(5.4365)/(2) = 2.71825`

At x = 5

`y = 2e^(0.5(5)) =24.3649\\\\\text{Senstivity} = \displaystyle(24.3649)/(5) = 4.8729`

At x = 10

`y = 2e^(0.5(10)) =296.8263\\\\\text{Senstivity} = \displaystyle(296.8263)/(10) = 29.6826`