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.

1) Solution x = 1, y = 3

2) The solution represent the temperature at which the number of visitor is equal to the number of people who leave early the park.

Explanation:

The very same graph copied by you gives the answer to the first question. The intersection point of the curve f(x) = 3^x and the line g(x) = - x + 4 is the solution  to the two functions.

You can read on the graph the coordinates of the point of intersection, they are x = 1, y = 3, and that is the solution.

You can proove by making substituting the x-coordinate value in both functions:

x = 1 => f(x) = 3^x = 3^1 = 3

x = 1 => g(x) = - x + 4 = - 1 + 4 = 3

Which prooves that the solution is x = 1, y = 3.

That point represent the temperature at which the number of visitors is equal to the number of people who leave the park early.