## Estimate the instantaneous rate of growth in 2004 by taking the average of two average rates of change.

Step-by-step solution-:

The **average growth rate** is given by:

\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}

Instantaneous Rate of growth in 2004 is equal to average

Growth rate of 2002 and 2006:

Substitute x2=2006 and x1=2002 into the expression:

\frac{f(2006)-f(2002)}{2006-2002}

Substitute f(2006)=12440 and f(2002)=5886 into the expression:

\frac{12440-5886}{2006-2002}

After simplifying we get

1638.5

The average growth rate is given by:

1638.5~\text{locations per year}

The Instantaneous rate of growth in \textcolor{primary}{2004} is:

\textcolor{primary}{1638.5~\text{locations per year}}