Steve manages a skate park and he has been analyzing the attendance data. steve finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 5x. steve 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 + 6. the graph of the two functions is below. find the solution to the two functions and explain what the solution represents.

To graph the two functions, set arbitrary functions of x. As you set different values of x, you get their corresponding values of y. When you have both coordinates, you plot them as shown in the picture. The blue line represents the function f(x) = 5x, while the orange line represents the function f(x) = -x+6.

From the graph shown in the picture, the two lines intersect at point (1,5). To solve this analytically, set the system of equations:

y = 5x
y = -x + 6

Equating both equation of y,

5x = -x + 6
6x = 6
x = 1

Then, use any of the original equations: y = 5x = 5(1) = 5. Hence, the solution is (1,5). What does this solution mean? It means that when temperature is at 5 units, the people leaving and entering the small zoo are equal. Meaning, for every 1 person that comes in, another 1 leaves.