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?
A. p=4x+50
B. p-450=4(x-15)
C. p-15=4(x-450)
D. p=4x+15
To find the equation that gives the city's population x years after 2010, we need to use the information given in the problem and translate it into an equation.
Let's work through the problem step by step:
1. In 2010, the population is the starting point, so the population at that time is 0 years after 2010. We can plug this into the equation as a reference point.
2. In 2025, the population is projected to be 450,000 people. Since 2025 is 15 years after 2010 (2025 - 2010 = 15), we can plug this into the equation as another reference point.
Based on this information, we can determine that the equation should have the form p = 4x + k, where p is the population in thousands of people x years after 2010, and k is a constant.
Now let's plug in the two reference points:
1. In 2010 (0 years after 2010), the population is 0, so we have:
0 = 4(0) + k
0 = k
2. In 2025 (15 years after 2010), the population is 450,000, so we have:
450 = 4(15) + k
450 = 60 + k
450 - 60 = k
390 = k
Therefore, the equation that gives the city's population p (in thousands of people) x years after 2010 is:
p = 4x + 390
So the correct answer is option: D. p = 4x + 15