Question

The population of the US in 1850 was 23191876. In 1900, the population was 62947714.

a. assuming that the population grew exponentially, compute the grownth constant.

b. assuming continued growth at a constant rate, predict the population in 1950.

Answer 1

let t=0 correspond with the year 1850
then 1900 ---> t = 50
then 1950 ---> t = 100

population = a( e^(kt) ) , where a is the initial population and t is the number of years since 1850
23,191,876 = a e^0
a = 23,191,876

then:
62,947,714 = 23,181,876 e^(50k)
2.715384812 = e^(50k)
50k = ln(2.715384812 )
k = .019978673

in 1950
pop = 23,191,876 e^(100( .019978673))
= 170,927,267