Word problem help

Question

in 2003, the population of a certain country per sq mile of land area was 87. In 2000, the person per sq mile population was 84.3. Assume the relationship between years and persons per sq mile is a linear relationship.

 

A write an equation, in slope-intercept form, describing the relationship between year and persons per sq mile. Use ordered pairs of the form (x,y), where x is the number of years past 2000 and y is the persons per sq mile.

 

b. use the equation to predict the person per sq mile population in 2010

Answer 1

Hi Stanley, 

 

a) In order to determine the equation for this relationship, we need to first find the slope between these two values. There are two ways to do this: 

 

1. Create a graph

*Create a graph with the x-axis representing the years past 2000 (so 2000 would be 0 and 2003 would be 3 and so on)

*Use the fact that slope=rise/run to get slope=2.7/3 (because we rise 87-84.3=2.7 and run 3 (from 2000 to 2003), and 2.7/3=27/30=9/10

*Plug this and the point (0, 84.3) into the formula y=mx+b to find the y-intercept of your equation

--> 84.3=(9/10)(0)+b --> b=84.3

So, your equation can be written now as y=(9/10)x+84.3

 

[Note: To check, if you plug in 3 you should get 87, and you do, so it works!]

 

2. Use the slope formula

Alternatively, you could have did slope=(y₂-y₁)/(x₂-x₁)=(87-84.3)/(3-0)=2.7/3=9/10

The process here would be the same as above

 

b) Here, just plug 10 into the equation above (since 10 is the number of years 2010 is after 2000, or 2010-2000=10). Doing this we get:

y=(9/10)(10)+84.3=9+84.3=93.3

So, in 2010 we have 93.3 people per sq mile!

 

Well, I hope this helps. Have a good one!

 

Matt