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.
c) Use the trapezoidal rule with n=4 to estimate: ∫ S(t)dt
d) Using correct units, explain the meaning of: ∫ S(t)dt in terms of cola consumption.
Thanks so much