Question

Steve is managing a skate park and has been analyzing the attendance data. Steve has found that the number of visitors increases exponentially as the temperature increases. Steve has also found a linear equation that models the number of people who leave the park early depending on the temperature. Describe how Steve can combine these two functions into a new function and explain what that function would predict.

Answer 1

The new function that was from a combination of two functions is N = a^t -(mt + b). N is the total number of visitors. The first function is the representation of the number of visitors that increases exponentially through time. Second equation is linear which was derived from y= mx + b.

Answer 2

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