Refer to Exercise 35 on page 704 for a description of a study about beer froth. Let E, A, and B be the heights (in centimeters) of froth for an Erdinger Weissbier, an Augustinerbräu München, and a Budweiser Budvar, all at x minutes after having been poured.

a. Find exponential regression equations for x and E, x, and A and x and B.
b. Find the vertical intercept for each of the three models. On the basis of your results, which beer had the most froth just after the beer was poured? Is that what actually happened? Explain.
c. What is the percentage rate of decay per minute for the mean height of froth of each of the three beers? Which beer had the greatest mean-height decay of froth? How you can tell this by inspecting Table 56 on page 704?
d. The researcher used a cylindrical beer mug. Why is it important that a cylindrical mug was used rather than a glass whose width varies from top to bottom?
e. The volume of a cylinder is given by V = πr2h, where r is the radius of the circular base and h is the height. The radius of the circular base of the beer mug was 3.6 centimeters. Predict the mean volume of froth 5.5 minutes after a Budweiser Budvar is poured.

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Table 56 Times and Mean Heights of Beer Froth Mean Height of Froth (centimeters) Time minutes) Weissbier Erdinger Augustinerbräu Budweiser Budvar 14.0 9.3 20 170 3.2 10.7 8.9 7.5 München 14.0 8.5 6.0 4.4 2.9 1.3 0.7 3.5 2.0 0.9 5.2