Q:

A lake was stocked with 360 trout. Each year, the population decreases by 10. The population of trout inthe 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 theintercepts.

Accepted Solution

A:
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 figurePart C) see the explanationStep-by-step explanation:Part A) Find the interceptsLetx ----> the number of yearsf(x) ----> the population of trout in the lakewe have[tex]f(x)=360-10x[/tex]This is a linear function in slope intercept form[tex]f(x)=mx+b[/tex]wherem is the slope or unit rateb is the y-intercept or initial valueIn this problem we have[tex]m=-10\ \frac{trout}{year}[/tex] ---> is negative because is a decreasing function[tex]b=360\ trouts[/tex] ---> initial valueThe y-intercept is the point (0,360)Find the x-interceptThe x-intercept is the value of x when the value of f(x) is equal to zerosoFor f(x)=0[tex]0=360-10x[/tex]Solve for x[tex]10x=360\\x=36[/tex]The x-intercept is the point (36,0)Part B) Graph the functionPlot the intercepts and join the points to graph the linesee the attached figurePart C) Complete the interpretation of the  interceptsThe x-intercept is the value of x when the value of f(x) is equal to zeroIn this context, the x-intercept is the number of years, when the population of trouts is equal to zerosoIn 36 years, the population of trouts will be equal to zeroThe y-intercept is the value of f(x) when the value of x is equal to zeroIn this context, the y-intercept is the population of trouts when the number of years is equal to zerosoInitially the population of trouts in the lake was 360 trouts