It is given that the initial population observed is 25 000 and that the population will decrease by 1000 each year. If we let x represent the number of years that the population has been tracked, we can write an expression that will give us the decrease in population per year.
1000x
Subtracting this product from the initial total will give us y, which is the polar bear population for any year. Now we can write the equation.
y=25 000-1000x
⇕
y=- 1000x +25 000
We will graph the equation that is written in slope-intercept form. The y-intercept of the equation is (0,25 000). To graph the equation, let's arbitrarily choose another point where x=10.
By using the points (0,25 000) and (10,15 000) we can graph the equation. Note that the number of years that the population has been tracked and the polar bear population cannot be negative.
Graphing an equation helps us to conceptualize the situation. For this exercise, we want to find the year that polar bears become extinct, which means we want to find the point where y=0. That point is called the x-intercept. We will substitute 0 for y to find the year that polar bears become extinct.
After 25 years, the population becomes 0. We can also see from the graph that for the value of x=25, the population reaches 0. That means, 25 years after 2005 (in 2030) the species will go extinct.
