1. The general form of the population equation is:
P = P_0(1+r)^t
Where:
P is the population at time t
P_0 is the initial population
r is the growth rate, expressed as a decimal
t is the number of years
Since P_0 = 22,000, r = 0.03, and t is measured in years from 2010, the equation is:
P = 22,000(1.03)^t
2. When t = 20 (for 2030), the population is:
P = 22,000(1.03)^20
= 31,890
3. We want to find the year when P exceeds 2 × 22,000 = 44,000.
Setting the equation equal to 44,000 and solving for t:
44,000 = 22,000(1.03)^t
(44,000/22,000) = (1.03)^t
2 = (1.03)^t
Taking the log base 1.03 of both sides:
log1.03(2) = t
t = 26.16
So the first year the population is more than double the 2010 population will be around 2036.