Linear Decrease

Question

the population of a town today is 20000 people.

(a) If the population decreases linearly and the decrease is 9% in the first year, what will the town's population be in 10 years?

Answer 1

Linearly means it goes down by the same amount each year (not percent, but amount). 9% of 20,000 = (0.09)(20,000) = 1800. This means, each year the population goes down by 1800 people.

There are lots of ways to get the answer.

1) You could create an equation where "x" is the number of years and "y" is the population and use the point-slope form, with the point (0, 20000) and the slope -1800. Then the equation is y - 20000 = -1800(x - 0) which simplifies to y = 20000 - 1800x. Then you could plug in x = 10 to get the answer.

2) You could just say: After 1 year the population would be 20,000 - 1800. After 2 years the population would be 20,000 - (2)(1800). After 10 years the population would be 20,000 - (10)(1800)

Either way, the answer is 2000