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}}