What is the base (common ratio) of the exponential expression y = 40 × (0.75)³?

What is the base (common ratio) of the exponential expression y = 40 × (0.75)³?

• A. 0.50
• B. 0.75
• C. 1.00
• D. 1.25

Answer: (B)

In an exponential expression written as a × r^n, the base (or common ratio) is the number r that gets raised to a power. In y = 40 × (0.75)³, the base is 0.75 because that is the number being raised to the third power. The 40 is the starting amount, not the base. Since 0.75 is less than 1, multiplying by it three times shrinks the value: (0.75)³ = 0.421875, so y = 40 × 0.421875 = 16.875.

In an exponential expression written as a × r^n, the base (or common ratio) is the number r that gets raised to a power. In y = 40 × (0.75)³, the base is 0.75 because that is the number being raised to the third power. The 40 is the starting amount, not the base. Since 0.75 is less than 1, multiplying by it three times shrinks the value: (0.75)³ = 0.421875, so y = 40 × 0.421875 = 16.875.