Hi, I am studying neoclassical growth theory and want to clarify what an exogenous increase in technology, A , means. (Please correct me if I’m…

Hi, I am studying neoclassical growth theory and want to clarify what an exogenous increase in technology,
, means. (Please correct me if I’m wrong):
When
increases to
, technological growth is positive where
 > 0
This will cause the production function curve to shift up to where y = f(k, A2)
So when the economy reaches steady state at
, does that mean that technological growth is zero,
 = 0
, again until there is another exogenous increase of
What is happening in the economy as it is trying to reach to a new steady state with
?
Does this mean that there must always be exogenous increases of
to
A3
,
A4
, … for
, so there is annual growth in the economy (since at steady state growth of capital = 0, and
ŷ = Â
)?
I am not sure if I have a wrong understanding of exogenous tech change. Would really appreciate some help!