Problem
An investment was worth $\$ 3,845$ in 1994 . In 1998 , its value was $\$ 5,097$. Find and interpret the average rate of change in value per year. A. The average rate of change is 3,845 . This means that the value of the investment increased by $\$ 3,845$ per year during these years. B. The average rate of change is 6,349 . This means that the value of the investment increased by $\$ 6,349$ per year during these years. C. The average rate of change is 313 . This means that the value of the investment decreased by $\$ 313$ per year during these years. D. The average rate of change is 313 . This means that the value of the investment increased by $\$ 313$ per year during these years.
Solution
Step 1 ：The problem is asking for the average rate of change in value per year of an investment that was worth $3,845 in 1994 and $5,097 in 1998.
Step 2 ：The average rate of change is calculated by taking the difference in the final and initial values and dividing by the difference in the final and initial times.
Step 3 ：In this case, the final value is $5,097, the initial value is $3,845, the final time is 1998, and the initial time is 1994.
Step 4 ：So, the average rate of change is calculated as \((5097 - 3845) / (1998 - 1994)\).
Step 5 ：This simplifies to \(313\).
Step 6 ：Final Answer: The average rate of change is \(\boxed{313}\). This means that the value of the investment increased by $313 per year during these years.
