Question

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 g(x) = −x + 6. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.

Answer 1

(1,5)

Explanation:

The graphs intersect at (1,5). At this point, the temperature change is 1 degree and the number of visitors is equal to those leaving early, which is 5 visitors.

Answer 2

• (1, 5)

Explanation:

Both of the graphs include infinite number of points.

The solution is the common point that belongs to both of the graphs, their intersection, which is the point (1, 5)

This is the point when the temperature change is positive 1 degree. At this point number of visitors is equal to number of those leaving the part early (5 visitors).