Question

2. In 2010, the population of a town is 8500. The population decreases by 4.5% each year.

(a) Write an equation to find the population of the town t years after 2010.

(b) In what year will the population of the town be 7000? Show your work.

Answer 1

If the population of a certain town decreases by 4.5% each year, we form a geometric sequence with first term equal to 8,500 and r equal to 0.955.

(a) The equation is then,

An = (8,500)(0.955)^n

Where n is the number of years.

(b) Substituting 7000 to An and solving for n,

7000 = 8500*(0.955)^n

The value of n from the equation is 4.2 years.