Logistic models .. Calculus, relative growth rate?

Question

The museum of science in Boston displays a running total of the U.S. population. On May 11, 1993, the total was increasing at the rate of 1 person every 14 sec. The displayed population figure ate 3:45 pm that day was 257,313,431. Assume that the relative growth rate is constant.
a. What is the relative growth rate per year (365 days)?
b. At this rate, what will the US population be at 3:45 pm Boston time on May 11, 2001?

Answer 1

A constant rate of growth defines the exponential function:
http://en.wikipedia.org/wiki/Exponential_function

Just as a side note, part a can be looked at as a compound interest problem: you know the interest rate for a period of 14 seconds (1/257,313,431) and want the annual return. So you might want to look at:
http://en.wikipedia.org/wiki/Compound_interest

By why do you call this "Logistic models"? The classic Logistic Model is an alternative to the simple exponential model:
http://www.ento.vt.edu/~sharov/PopEcol/lec5/logist.html