Question: The rate of consumption of bottled water in the U.S. can be modeled by the equation \(R(t)=C e^{k t}\), where \(R\) is measured in billions of gallons of bottled water per year and \(t\) is measured in years from the beginning of 1990 .

1. If the consumption rate doubles every 4 years, and the consumption rate at the beginning of 1990 was 2 billion gallons per year, find \(C\) and \(k\).
2. Find the average rate of consumption over the 6 -year period beginning January 1, 2000. Indicate units of measure.
3. Use the trapezoidal rule with 3 equal subdivisions to estimate \(\int_{10}^{16} R(t) d t\).
4. Using correct units, explain the meaning of \(\int_{10}^{16} R(t) d t\) in terms of bottled water consumption.
5. If the average amount of plastic used per gallon of bottled water is 5.3 ounces, what was the total amount of plastic used for bottled water in the US during the year 2005?

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