1. The rate of change of the altitude of a hot-air balloon is given by r(t) = t^3-4t^2+6 on [1,8]. Which of the following expressions gives the change in altitude of the balloon during the time the altitude is decreasing? (work too please)

3.514 8 2.667 3.514 2.667

a) ∫ r(t) dt b) ∫ r(t)dt c) ∫ r(t)dt d) ∫ r'(t)dt e) ∫ r'(t)dt

1.572 0 0 1.372 0

2. The rate of consumption of cola in the United states is given by S(t)= Ce^kt, where S is measured in billions of gallons per year andf t is measured in years from the beginning of 1980.

a) The consumption rate doubles every 5 years and the consumption rate at the beginning of 1980 was 6 billion gallons per year (when t=0, S(t)= 6). Find C and k.

b) Find the average rate of consumption of cola over the 10 year time period beginning Janurary 1, 1983. Indicate units of measure.

7

c) Use the trapezoidal rule with n=4 to estimate: ∫ S(t)dt

5

7

d) Using correct units, explain the meaning of: ∫ S(t)dt in terms of cola consumption.

5

Thanks so much