Question

Absolute vs relative rate of change

Answer 1

My understanding was that when one wished to inspect a relative rate of change you would take the differential and divide by the original function e.g. \[ \frac{ f'(x) }{ f(x) }\] But in my notes from class my teacher has got that an absolute growth rate is equal to \[\frac{ dY }{ dt }=\lim \Delta t \rightarrow 0 \frac{ Y(t + \Delta t)-Y(t) }{ \Delta t }\] and that the relative rate of change is then \[\frac{ dY/dt }{ Y }=\lim \Delta t \rightarrow0 \frac{ \frac{ Y(t+\Delta t)-Y(t) }{ Y(t) } }{ \Delta t }\] but I don't see why the Y(t) isn't in the denominator as opposed to the delta t

Answer 2

@jim_thompson5910 @jdoe0001 @tkhunny @Compassionate any thoughts? Help really appreciated

Answer 3

@aum @perl @ShadowLegendX

Answer 4

?? Why does it matter? \(\dfrac{\dfrac{Stuff}{Y}}{\Delta} = \dfrac{\dfrac{Stuff}{\Delta}}{Y} = \dfrac{Stuff}{Y}\cdot\dfrac{1}{\Delta}\)