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 the equation that gives the city's population p ( in thousands of people) x years after 2010?
The population by 4000 for 15 years, or 60,000
So, it must have been 450,000-60,000 = 390,000 in 2010
p(x) = 390 + 4x
To find the equation that gives the city's population, we can start by establishing a relationship between the population and the number of years since 2010.
Let's denote the number of years since 2010 as "x". We know that the population of the city in 2010 is not given, so we need to take that into account when setting up the equation.
Since the population increases by 4,000 people each year, we can express the population as:
P = 4,000x + C
Where P represents the population (in thousands of people) x years after 2010, and C represents the population in the year 2010.
In 2025, x = 2025 - 2010 = 15 years after 2010. At that time, the projected population is 450,000 people.
Substituting these values into the equation, we have:
450 = 4,000(15) + C
Now we can solve for C:
450 = 60,000 + C
C = 450 - 60,000
C = -59,550
Finally, we can rewrite the equation with the determined value of C:
P = 4,000x - 59,550
So, the equation that gives the city's population p (in thousands) x years after 2010 is P = 4,000x - 59,550.