The United States population in 1800 was 5,308,000 and in 1900 was 76,212,000. Assume t= 0 in 1800 and the population grew at a rate proportional to its size.
a) Find P(t), the number of people in the United States at time t according to this data. (Use an exact value for the rate, k.) P(t)
b) Using this model, predict the U.S. population in the year 2000. Round to the nearest person. people
c) The actual population of the U.S. in 2000 was 281,422,000. Which of the following is NOT true.
A) It is likely that the growth rate of the U.S. population slows as the population becomes larger.
B) The model used here for the population grows without bound.
C) The exponential growth model used overpredicts what the population in the U.S. over time will be.
D) The U.S. population outpaces the predictions of this model.