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.
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.
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)
Central Limit Theorem states that population with mean and standard deviation and if the sample size is large then the distribution of sample mean will be will be normally distributed. The central limit theorem holds assumptions that the factors to be considered when assessing central limit theorem is sample size.
