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 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.

Answer 1

Answer:Suppose that the equations are:

The number of people increases exponentially as the temperature increases, so we can write this as a simple exponential relation.

N(T) = a0*r^(T)

Also, the number of people that leaves the park as the temperature increases are:

M(T) = a*T + b

So the combination of these equations can say the number of people that are arriving to the park minus the number of people that are leaving, this would be:

N(T) - M(T) = total change in the park population as the temperature changes = C(T)

C(T) = a0*r^(T) - a*T - b

Explanation: