Let's break down each of the three parts of this question.

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(i) What were the sales in 2011?

We are told that bottled water sales increased by 6.7% in 2012 and the total sales for 2012 were $11.8 billion.

Let $x$ represent the sales in 2011. The 6.7% increase means that the sales in 2012 are 106.7% of the sales in 2011:

$\text{2012 sales} = \text{2011 sales} \times (1 + 0.067)$ $11.8 = x \times 1.067$

To solve for $x$, divide both sides by 1.067:

$x = \frac{11.8}{1.067} \approx 11.06$

So, the sales in 2011 were approximately $11.1 billion (rounded to the nearest tenth).

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(ii) Estimate the per capita consumption from 2011.

We are told that in 2012, the total U.S. bottled water consumption was 9.67 billion gallons and the average person drank 30.8 gallons. First, calculate the total U.S. population in 2012:

$\text{Population} = \frac{\text{Total consumption}}{\text{Per capita consumption}} = \frac{9.67 \text{ billion gallons}}{30.8 \text{ gallons/person}} \approx 314.9 \text{ million people}$

Now, estimate the per capita consumption for 2011. We know that the total bottled water consumption in 2011 was 9.1 billion gallons. Using the same population estimate for 2011:

$\text{Per capita consumption in 2011} = \frac{9.1 \text{ billion gallons}}{314.9 \text{ million people}} \approx 28.9 \text{ gallons}$

So, the estimated per capita consumption in 2011 was approximately 28.9 gallons (rounded to the nearest tenth).

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(iii) Quantify the bottled water consumption increase from 2011 to 2012 in terms of absolute change.

The total consumption in 2011 was 9.1 billion gallons, and the total consumption in 2012 was 9.67 billion gallons. The absolute change in consumption is:

$\text{Change in consumption} = 9.67 - 9.1 = 0.57 \text{ billion gallons}$

So, the increase in bottled water consumption from 2011 to 2012 was 0.57 billion gallons (rounded to the hundredths place).

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Summary of Answers:

• (i) Sales in 2011: $11.1 billion
• (ii) Per capita consumption in 2011: 28.9 gallons
• (iii) Absolute increase in consumption: 0.57 billion gallons

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Would you like more details on any of these calculations or have any follow-up questions?

Related Questions:

1. How would the total U.S. bottled water consumption change if the per capita consumption increased by 10% in 2013?
2. If the 6.7% sales increase continued for the next three years, what would be the sales in 2015?
3. How can you estimate the per capita consumption for a different country given similar data?
4. If the average price per gallon of bottled water increased by 5% in 2012, how would that impact the total sales?
5. How can you calculate the growth rate for a different beverage category based on similar data?

Tip:

When calculating percentage increases, remember the formula:
$\text{New Value} = \text{Old Value} \times (1 + \text{Percentage Increase})$