exponential growth

Question

The population of Adamsville grew from 6,000 to 13,000 in 8 years. Assuming uninhibited exponential growth, what is the expected population in an additional 5 years?

Answer 1

N = P ( 1 + r )ⁿ

13000 = 6000 ( 1 + r )⁸

Log 13/6 = 8 Log ( 1+r )

0.336 / 8  = Log ( 1+r )

0.042 = Log ( 1+r )

10^(.042) = 1 + r    after exponentiating both sides

1.102  1 + r

r = .102 

 

In 5 more years

N = 13000 ( 1 + .102 )⁵

N = 13000 ( 1.622 )

N = 21083