Annual sales of bottled water in the country in the period 1993-2003 could be approximated by the function below, where t is time in years since 1990. Were sales of bottled water accelerating or decelerating in 2000? How fast?

R(t) = 10 t**2 + 100 t + 2400 text( million gallons ) \(3<=t<=13\)

Something wrong with the answer Damon gave you on

Tuesday, November 29, 2011 at 5:42am?

To determine if the sales of bottled water were accelerating or decelerating in 2000, we need to calculate the second derivative of the function R(t) with respect to time. The second derivative gives us information about the rate of change of the rate of change, or the acceleration.

First, let's find the first derivative of R(t):
R'(t) = 20t + 100

Now, let's find the second derivative:
R''(t) = 20

Since the second derivative is a constant value of 20, it means that the acceleration is constant and not changing over time. Therefore, we can conclude that the sales of bottled water were neither accelerating nor decelerating in the year 2000.

The constant acceleration of 20 (million gallons per year squared) tells us that for each year, the sales of bottled water were increasing by a constant rate of 20 million gallons per year.