Question

A lake was stocked with 360 trout. Each year, the population decreases by 10. The population of trout in
the lake after x years is represented by the function f(x) = 360 - 10x.
Find the intercepts, then use the intercepts to graph the function. Complete the interpretation of the
intercepts.

Answer 1

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

$f(x)=360-10x$

This is a linear function in slope intercept form

$f(x)=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

$m=-10\ \frac{trout}{year}$ ---> is negative because is a decreasing function

$b=360\ trouts$ ---> initial value

The y-intercept is the point (0,360)

Find the x-intercept

The x-intercept is the value of x when the value of f(x) is equal to zero

so

For f(x)=0

$0=360-10x$

Solve for x

$10x=360\\x=36$

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