Question

A town's population has been growing linearly. In 2003 the population was 63,000. The population has been growing by 1200 people each year.

Write an equation for the population, P, x years after 2003.

P = ____________

Use the formula to find the population in 2009: ___________

Answer 1

The equation for the linear population growth is P = 63,000 + 1,200x. For the population in 2009, x equals 6, and substituting this into the equation gives us a population of 70,200 people.

Step-by-step explanation:

To write an equation for the population, P, x years after 2003, given that the initial population is 63,000 and it increases linearly by 1,200 each year, we can use the linear growth formula:

P = P0 + r × x

Where P0 is the initial population, r is the rate of growth per year, and x is the number of years after 2003. Using the given figures:

P = 63,000 + 1,200x

To find the population in 2009, we calculate x as the number of years since 2003, which is 2009 - 2003 = 6. Substituting x = 6 into the equation:

P = 63,000 + 1,200 × 6

P = 63,000 + 7,200

P = 70,200

So, the population of the town in 2009 was 70,200 people.