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 answerl
To determine the equation, we can use the information given.
First, let's break down the problem:
- The population in 2010 is the starting point, meaning x = 0 in the equation.
- The population is projected to be 450,000 people in 2025, which is 15 years after 2010, so x = 15 in the equation.
- The population increases by 4,000 people each year.
Now, let's form the equation:
Since the increase is in thousands of people, we need to divide the increase by 1,000.
Starting with the population in 2010, let's represent it as p.
Then, the population x years after 2010 can be represented as p + 4000x.
To determine the value of p, we can substitute the known value for x when the population is 450,000 people in 2025.
So, when x = 15, p + 4000(15) = 450.
Simplifying this equation, we have p + 60,000 = 450.
Subtracting 60,000 from both sides of the equation, we get p = 450 - 60,000.
Simplifying further, p = -59,550.
Now, since we want the equation in terms of x and p, we can substitute the value of p back into p + 4000x to get the final equation.
p + 4000x = -59,550 + 4000x.
To make the equation look like the given answer, we can rearrange it:
p - 450 = 4000x + 4000(-15).
Simplifying further, we have p - 450 = 4000x - 60,000.
Therefore, p – 450 = 4(x – 15) is the equation that gives the city's population p (in thousands of people) x years after 2010.