Steve manages a skate park and he has been analyzing the attendance data. Steve finds that the number of visitors increases expo
nentially 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. (10 points)
Both of the graphs include infinite number of points.
The solution is the common point that belongs to both of the graphs, the intersection point.
We can see it 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.
When we scale an object by a scale factor, the side lengths become the scale factor times bigger than the previous sides. Therefore, with a scale factor of 6, the side lengths would be multiplied by 6.