Thread: stuck on Derivatives of exponential functions

The number of XM satellite Radio subscribers, in millions can be approximated by
f(t)=0.028(3.824)^(t-2001),where t is the year.

Find the instantaneous rate of change in the number of XM satellite radio subscribers in 2006 years.


I got f'(2006)=99.3968 ,but I don't know how to give the unit of that answer.

Originally Posted by shannon1111

The number of XM satellite Radio subscribers, in millions can be approximated by
f(t)=0.028(3.824)^(t-2001),where t is the year.

Find the instantaneous rate of change in the number of XM satellite radio subscribers in 2006 years.


I got f'(2006)=99.3968 ,but I don't know how to give the unit of that answer.

The units can be though of as

so in words the change in f over the change in t

Since f represents the number of subsribers per year and t represents time we get

The change in the number of subscribers per year.( in Millions)

Originally Posted by TheEmptySet

The units can be though of as

so in words the change in f over the change in t

And so has the units of f divided by the units of t

Since f represents the number of subsribers per year

No! f represents the number of subscribers (in a particular year)

and t represents time we get

t does not just "represent time", t is measured in years.

The change in the number of subscribers per year.( in Millions)

So df/dt is measured in "subscribers per year".