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 f(x) = −x + 4. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.
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.
The solution to this set of functions is (1,3) or x=1 and y=3. This solution represents the temperature at which the number of visitors is equal to the number of people who leave the park early.
Since it is graphed, and by the basic rules of functions, we know that the intersection of these two functions will be the answer. When you look at the graph, you can see the two functions intersect at (1,3). You can also check if this is correct by substituting these values back into these functions. For example, 3=3^1 is true and so is 3=-1+4, therefore, the solution is correct.
