G.29
The entrance of the Aquarium of Americas in New Orleans has a gigantic building-size curve called a logarithmic spiral. Find out how to construct a logarithmic spiral, and write a paper about what you learned. Why do you suppose it would appear on the front of an aquarium?
G.30
If we assume that the world population grows exponentially, then it is also
reasonable to assume that the use of some nonrenewable resource (such as petroleum)
will also grow exponentially. In calculus, it is shown that for some constant
k, under these assumptions, the formula for the amount of the resource,
A, consumed from time t = 0 to t = T is given by the
formula
where r is the relative growth rate of annual consumption.
a. Solve this equation for T to find a formula for life expectancy
of a particular resource.
b. According to the Energy Information Administration, the annual world
production (in billions of barrels per day) of petroleum is shown in the
following table:
| Year: | 1975 | 1980 | 1985 | 1990 | 1995 | 2000 | 2003 |
| Quantity: | 52.42 | 62.39 | 52.97 | 60.90 | 61.85 | 66.03 | 67.00 |
Find an exponential equation for these data.
c. If in 1998, the world petroleum reserves are 2.8 trillion barrels, estimate the life expectancy for petroleum.