The formula to calculate the average rate (AVR) is:
\[ AVR = \frac{IR + FR}{2} \]
Where:
Let's say the initial rate is 10, and the final rate is 20. Using the formula:
\[ AVR = \frac{10 + 20}{2} \]
We get:
\[ AVR = 15 \]
So, the average rate (\( AVR \)) is 15.
Definition: The average rate of a reaction in chemistry is the change in concentration of a reactant or product per unit time.
Formula: \( \text{Average Rate} = \frac{\Delta \text{Concentration}}{\Delta \text{Time}} \)
Example: \( \text{Average Rate} = \frac{0.5}{10} \)
Definition: The average rate is the total change in a quantity divided by the total time taken.
Formula: \( \text{Average Rate} = \frac{\Delta \text{Quantity}}{\Delta \text{Time}} \)
Example: \( \text{Average Rate} = \frac{100}{20} \)
Definition: In calculus, the average rate of change of a function over an interval is the change in the function value divided by the change in the interval.
Formula: \( \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \)
Example: \( \text{Average Rate of Change} = \frac{f(5) - f(2)}{5 - 2} \)
Definition: The annual percentage rate (APR) is the annual rate charged for borrowing or earned through an investment.
Formula: \( \text{APR} = \left( \frac{\text{Interest Paid}}{\text{Principal}} \right) \times \frac{365}{\text{Days in Loan Term}} \times 100 \)
Example: \( \text{APR} = \left( \frac{50}{1000} \right) \times \frac{365}{30} \times 100 \)
Definition: The average annual rate is the average rate of return per year over a period.
Formula: \( \text{Average Annual Rate} = \left( \frac{\text{Final Value}}{\text{Initial Value}} \right)^{\frac{1}{n}} - 1 \)
Example: \( \text{Average Annual Rate} = \left( \frac{2000}{1000} \right)^{\frac{1}{5}} - 1 \)
