The initial rate of a reaction `A+B to` Products is doubled when the concentration of A is doubled and increases eight fold when the initial concentration of both A and B are doubled. State the order of the reaction with respect to A and with respect to B. Write the rate equation.

Explanation

To solve the problem, we need to determine the order of the reaction with respect to reactants A and B based on the given information about the changes in the reaction rate when the concentrations of A and B are altered.

### Step-by-Step Solution:

1. **Understanding the Rate Law**:
The rate law for the reaction \( A + B \rightarrow \text{Products} \) can be expressed as:
\[
\text{Rate} = k [A]^x [B]^y
...