A population grows from 11,000 to 19,000 in three years.

Question

A. Assuming the growth is exponential, find the annual growth rate.

B.  Assuming the growth is exponential, find the continuous growth rate.

Answer 1

PART A: Exponential Growth compounded annually

Use this equation: A = A0*(1+r)^t

19000 = 11000(1+r)^3

(19/11)^(1/3) = (1+r)

1.19983 ~ (1+r)

0.1998 ~ r

PART B: Exponential Growth, compounded continuously

Use this equation: A = A0*e^(rt)

19000 = 11000*e^(3r)

(19/11) = e^(3r)

ln(19/11) = 3r

r = ln(19/11) / 3

r ~ 0.18218