Calculating Time Constant for First-Order Instrument Step Change

[the_d]

The problem is for a first-order instrument exposed to a step change of 100 units. If after 1.2 seconds the instrument indicated 80 units, estimate the instrument time constant.

the problem I am having is chosen the correct formula for the time constant, any suggestions?

 

[SGT]

The problem is for a first-order instrument exposed to a step change of 100 units. If after 1.2 seconds the instrument indicated 80 units, estimate the instrument time constant.

the problem I am having is chosen the correct formula for the time constant, any suggestions?

The formula is
$$x(t) = A(1 - e^{-t/T})$$
where

• x(t) is the value at time t
• A is the final value
• T is the time constant

 

[SGT]

I don't know why my LaTex formula didn't work. Here it goes in text form:
x(t) = A(1 - exp(-t/T))

 

[the_d]

much thanks