Answer:
Part A) The y-intercept is the point (0,360) and the x-intercept is the point (36,0)
Part B) The graph in the attached figure
Part C) see the explanation
Step-by-step explanation:
Part A) Find the intercepts
Let
x ----> the number of years
f(x) ----> the population of trout in the lake
we have
This is a linear function in slope intercept form
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem we have
---> is negative because is a decreasing function
---> initial value
The y-intercept is the point (0,360)
<em>Find the x-intercept</em>
The x-intercept is the value of x when the value of f(x) is equal to zero
so
For f(x)=0
Solve for x
The x-intercept is the point (36,0)
Part B) Graph the function
Plot the intercepts and join the points to graph the line
see the attached figure
Part C) Complete the interpretation of the intercepts
The x-intercept is the value of x when the value of f(x) is equal to zero
In this context, the x-intercept is the number of years, when the population of trouts is equal to zero
so
In 36 years, the population of trouts will be equal to zero
The y-intercept is the value of f(x) when the value of x is equal to zero
In this context, the y-intercept is the population of trouts when the number of years is equal to zero
so
Initially the population of trouts in the lake was 360 trouts
