The population of a city increases by 4,000 people each year. In 2025, the population is projected to be 450,000 people. What is an equation that gives the city’s population p (in thousands of people) x years after 2010?
answer p – 450 = 4(x – 15)
how did you get the answer
To determine the equation for the city's population, we need to consider the following information:
1. In 2010, x years before 2025, the population was 450,000 - 4,000x (since it increases by 4,000 people per year).
2. We want our equation to represent the population in thousands of people, so we divide the population obtained in point 1 by 1,000.
Based on these considerations, the equation can be written as:
p = (450,000 - 4,000x) / 1,000
Simplifying this equation gives:
p = 450 - 4x
However, since we want to represent the years after 2010, we need to adjust the equation. In 2010, x = 0, so the equation should be shifted 5 years forward. This gives:
p = 450 - 4(x - 5)
Simplifying further:
p = 450 - 4x + 20
p = -4x + 470
Finally, we can rearrange the equation to match the given answer:
p - 450 = -4(x - 15)
p - 450 = -4x + 60
p = -4x + 510
So, the equation "p – 450 = 4(x – 15)" that you mentioned is not correct. The accurate equation should be "p = -4x + 510".