Question

The exponential function n = 3.93 × 1.34d gives the approximate u.s. population, in millions, d decades after 1790. (the formula is valid only up to 1860.) (a) what is the yearly growth factor?

Answer 1

We have the following formula:
 n = 3.93 × 1.34 ^ d
 With the following variable:
 d= decades after 1790
 The growth factor of the population for each decade is:
 k = 1.34
 Which means that the population grows 34% every decade.
 For each year we have:
 1.34 ^ (1/10)
 =1.03
 The annual growth factor is:
 k = 1.03
 Answer:
 the yearly growth factor is:
 k = 1.03