Is saying "decreasing rate" the same as saying "rate is decreasing"?
I'm a AP calculus teacher grading a question that ask about the interpretation of the derivative of a rate. The answer key answer says, "...the rate of filling bottles is decreasing at a rate of 5.164 gal. per min. per min."
Someone wrote, "..the bottles are being filled at a decreasing rate of 5.164..."
I'm not 100% sure if that is logically equivalent to the correct answer.
Is saying, "rate of change is decreasing " logically equivalent to saying, "[filled] at a decreasing rate"??
Yes "Rate of change is decreasing" IS logically equivalent to a "decreasing rate" which is equivalent to saying in this case that $\frac{d^2V}{dt^2}=-5.164$.