185k views
3 votes
The population of a town is 101,702 in 2010. The population of the town decreased at an approximately constant rate and reached a population of 93,062 in 2020. What is the initial value (y-intercept)? people What is the slope? people per year Write an equation is slope-intercept form to represent the situation. y = x + Estimate the population of the town in 2025. people in 2025

User BitByteDog
by
8.4k points

1 Answer

2 votes

Final answer:

The initial value or y-intercept is the 2010 population of the town (101,702 people). The slope, representing the yearly population decrease, is -864 people per year. The population in 2025 is estimated to be 88,742 people based on the linear equation y = -864x + 101,702.

Step-by-step explanation:

We are looking to create a linear equation in the form of y = mx + b to represent the population decline over time. Here, y will represent the population of the town in a given year, x is the number of years since 2010, m is the slope of the line (change in population per year), and b is the y-intercept (the population at the starting year, which is 2010).

The initial value or y-intercept of our linear equation would be the population of the town at the start of our observation, which is 2010. In this case, it is 101,702 people.

To calculate the slope, we look at the change in population over the time period.

The decrease in population from 2010 to 2020 is from 101,702 to 93,062, which is a change of 101,702 - 93,062 = 8,640 over 10 years.

Therefore, the slope (m) is the change in population divided by the change in time, which is -8640/10 = -864 people per year.

Now, we can write the equation: y = -864x + 101,702.

To estimate the population of the town in 2025, we substitute x = 15 (since 2025 is 15 years after 2010) into our equation:
y = -864(15) + 101,702
This simplifies to y = -12,960 + 101,702

= 88,742 people in 2025.

User EggBender
by
7.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories