The Solution.
Given the exponential function below:
[tex]V(x)=500(1.5)^x[/tex]
The average rate of change over the interval [2,6] is given as below:
[tex]\text{Average rate of change =}\frac{V(6)-V(2)}{6-2}[/tex]
To find V(6):
[tex]V(6)=500(1.5)^6=500\times11.3906=5695.313[/tex]
To find V(2):
[tex]V(2)=500(1.5)^2=500\times2.25=1125[/tex]
So, substituting for the values of V(6) and V(2) in the above formula, we get
[tex]\begin{gathered} \text{Average rate of change over \lbrack{}2,6\rbrack =}\frac{5695.313-1125}{6-2} \\ \\ \text{ = }\frac{4570313}{4}=1142.578\approx1143\text{ visitors per week} \end{gathered}[/tex]
Thus, the correct answer is 1143 visitors p
