The length of time Y necessary to complete a key operation i

The length of time Y necessary to complete a key operation in the construction of houses
has an exponential distribution with mean 10 hours. The cost of completing the operation C
as a function of time is given by the formula C = 100 + 40Y + 3Y². Find the mean and
variance of C. Please be as specific as possible in your steps. I know this question has been answered before, but I am having some trouble understanding how to find Var[C].

Solution

mean = 100 + 40*10 + 3*10^2

mean = 800