Question

Verden had a population of 22,000 in 2010 and has been growing at a rate of 3% per year since then. 1. Write an equation to show the population P of Verdent years after 2010. 2. Find the population of Verden in 2030. 3. What would be the first year that the population is more than twice what it was in 2010.

Answer 1

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.