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

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:

$y = 2e^{0.5x}$

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

We define sensitivity as the ration of output to input.

$\text{Sensitivity} = \displaystyle\frac{\text{Out-put}}{\text{In-put}} = \frac{y}{x}$

At x  = 0

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

At x = 1

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

At x = 2

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

At x = 5

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

At x = 10

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