Final answer:
The percentage rate of decrease for the equation y = 42(0.913)^x is 8.7%, which is option D. The decrease is determined by subtracting the base of the exponential from 1 and converting it to a percentage.
Step-by-step explanation:
The question requires determining the percentage rate of increase or decrease for the exponential equation y = 42(0.913)x. This type of equation represents exponential decay, where the base of the exponential, 0.913, is less than 1. To find the percentage change, we need to understand that the base of the exponent (0.913) can be thought of as 1 minus the rate of decay (or decrease).
So, if we consider the base 0.913, it equates to a 1 - 0.913 = 0.087 decrease. To express this as a percentage, we multiply by 100%: 0.087 × 100% = 8.7%. Therefore, the equation has a 8.7% rate of decrease each time the variable x increases by 1.
The correct answer to the student's question is 8.7%, which corresponds to option D.