In the exponential expression y = 40 × (0.75)³, what is the initial amount?

In the exponential expression y = 40 × (0.75)³, what is the initial amount?

• A. 40
• B. 0.75
• C. 3
• D. 27

Answer: (A)

In this kind of expression, the starting amount is the number in front of the exponential part. The (0.75)³ represents applying a decay factor of 0.75 three times, so you begin with 40 and then multiply by 0.75 three times. Therefore, the initial amount is 40. (If you wanted the amount after three periods, you’d compute 40 × (0.75)³ ≈ 16.875.) The 0.75 is the per-period multiplier, and 3 is the number of periods, not the starting amount.

In this kind of expression, the starting amount is the number in front of the exponential part. The (0.75)³ represents applying a decay factor of 0.75 three times, so you begin with 40 and then multiply by 0.75 three times. Therefore, the initial amount is 40. (If you wanted the amount after three periods, you’d compute 40 × (0.75)³ ≈ 16.875.) The 0.75 is the per-period multiplier, and 3 is the number of periods, not the starting amount.