As an example, we work through the steps of this problem.

The average price of a condo in the downtown Hollywood area between $1995$ and $2005$ can be modeled by this equation.

where t is time in years $($t$=0$ corresponds to $1995).$ Determine the average price in $2004$ and the rate at which it is increasing or decreasing.

Solution:

To calculate the average price in $2004,$ t $=---0-949$ so we plug that into our equation since P represents average price.

To calculate the rate of increase or decrease, we take the derivative of P$.$ Since the derivative of the exponential function is itself, we can use the chain rule and get:

Since we are interested at the rate in $2004,$ we again can plug in $---409-9$ for t$.$

Since this is positive, this tells us the rate is $---$ increasing decreasing at a rate of $\mathrm{.}22---$ million dollars per month dollars per $10$ years million dollars per year condos per year $.$