exponential distribution question

I'm having trouble setting up the following equation:

The length of time $\displaystyle Y$ necessary to complete a key operation in the construction of houses has an exponential distribution with mean 10 hours. The formula $\displaystyle C=100+4Y+3Y^2$ relates to the cost of $\displaystyle C$. Find the mean of $\displaystyle C$.

initially would it be:

$\displaystyle \frac{1}{\beta}e^{-\frac{y}{\beta}} = \frac{1}{10}e^{-\frac{y}{10}}$

$\displaystyle \int^{\infty}_0 y \frac{1}{10}e^{-\frac{y}{10}} \times (100+4y+3y^2) \ dy$

then just integrate out?