Linear Algebra

Question

In one part of the? world, the sea lion population decreased approximately linearly from about 60 thousand in 1990 to about 24 thousand in 2003. Find the average rate of change of the sea lion population per year

Answer 1

Here's a detailed explanation. Rate of change aka slope aka m.

 

Rate of change = change in y / change in x.

 

Typically "time" is the "x" variable.

 

In this question, you are given "years" therefore years is the x variable.

 

rate of change = change in sea lions / change in years

 

population declined from 60000 to 24000 / in the years 1990 to 2003

 

y2 is 24000, y1 is 60000, x2 is 2003, x1 is 1990

 

m = y2 - y1 / x2 - x1

 

m = - 36,000 / 13 

 

m = - 3000

 

Matt

 

Answer 2

Turn the information into coordinate points.

 

Point = (time, population)

 

Point 1 = (2000 , 60000)

Point 2 = (2003 , 24000)

 

Find the slope between these points using the formula

 

m = (y₂ - y₁) / (x₂ - x₁)