# stuck on Derivatives of exponential functions

• Feb 21st 2009, 12:58 PM
shannon1111
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.
• Feb 21st 2009, 01:17 PM
TheEmptySet
Quote:

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 $\displaystyle \frac{\Delta f}{\Delta t}$

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)
• Feb 21st 2009, 04:39 PM
HallsofIvy
Quote:

Originally Posted by TheEmptySet
The units can be though of as $\displaystyle \frac{\Delta f}{\Delta t}$

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

Quote:

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

Quote:

and t represents time we get
t does not just "represent time", t is measured in years.

Quote:

The change in the number of subscribers per year.( in Millions)
So df/dt is measured in "subscribers per year".