the population of a city increases by 4,000 people each year. in 2050, 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?
Let "x" represent the number of years after 2010.
Since the population increases by 4,000 people each year, the population "p" (in thousands of people) x years after 2010 can be calculated as:
p = 4x + 400
Here, we add 400 to account for the population in 2010, which is 400,000 people (since it is given that the population in 2050 is projected to be 450,000 people).
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To find an equation that gives the city's population "p" (in thousands of people) "x" years after 2010, we need to first determine the initial population in 2010.
We know that in 2050, the population is projected to be 450,000 people, and the population increases by 4,000 people each year. Since we're looking for the population x years after 2010, the number of years between 2010 and 2050 is 2050 - 2010 = 40 years.
Let's denote the initial population in 2010 as "p₀" (in thousands of people). We can calculate the initial population using the following equation:
p₀ + (4,000 * 40) = 450,000
We multiply the rate of increase (4,000) by the number of years (40) and add it to the initial population to reach the projected population in 2050 (450,000).
Simplifying the equation, we have:
p₀ + 160,000 = 450,000
To isolate p₀ on one side, we subtract 160,000 from both sides:
p₀ = 450,000 - 160,000
p₀ = 290,000
Therefore, the equation that gives the city's population "p" (in thousands of people) "x" years after 2010 is:
p = 290,000 + 4,000x