Question

Shannon manages a small zoo and she has been analyzing the attendance data. Shannon finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 3x. Shannon also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by g(x) = −x + 4. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.

Graph increasing exponentially from the left, crosses the y axis at one and goes to infinity and intersects a linear graph that decreases and crosses the y axis at four and the x axis at four.

Answer 1

The solution to the two functions is (1, 3) and it represents the temperature at which the number of people visiting the zoo equals the number of people leaving the zoo.