There are two types of exponential functions: .exponential growth and exponential decay The base of an exponential growth function is
a number greater than one. The base of an exponential decay function is a number between 0 and 1.
Exponential functions are frequently used to model the growth or decay of a
population. You can use the y-intercept and one other point on the graph to write the equation of an exponential function.
Every ten years, the Bureau of the Census counts the number of people living
in the United States. In 1790, the population of the U.S. was 3.93 million. By 1800, this number had grown to 5.31 million.
Write an exponential function that could be used to model the U.S. population y in millions for 1790 to 1800. Write the equation in terms of x, the number of
decades x since 1790.
Assume that the U.S. population continued to grow at that rate. Estimate the
population for the years 1820, 1840, and 1860. Then compare your estimates
with the actual population for those years, which were 9.64, 17.06, and
31.44 million, respectively.
RESEARCH Estimate the population of the U.S. in 2000. Then use the Internet
or other reference to find the actual population of the U.S. in 2000. Has the
population of the U.S. continued to grow at the same rate at which it was
growing in the early 1800s? Explain.
If a typical computer operates with a computational speed s today, write an
expression for the speed at which you can expect an equivalent computer to
operate after x three-year periods.
Suppose your computer operates with a processor speed of 600 megahertz and you want a computer that can operate at 4800 megahertz. If a computer with that speed is currently unavailable for home use, how long can you expect to wait until you can buy such a computer?