given lognormal distribution, find expected value of its function I know that $Y(t)$ is a lognormal function with $$E[\log(Y(t)]=\log(Y_0)-10t$$ and $$Var(\log(Y(t))=2t$$
Given this information, how do I find $$E[(Y(t)+3)^2]?$$
I'm guessing I need to somehow use the formula for the continuous expected value, but I'm not sure how to put it all together
Any hints would be greatly appreciated!

You know the mean and variance of the underlying normal distribution.  I'll rewrite them as $\mu$ and $\sigma^2$ to save space: these are the stated functions of $t$. 
Then $E[Y(t)] = e^{\mu+\sigma^2/2}$ and $Var(Y(t)) = \left(e^{\sigma^2}-1\right)e^{2\mu+\sigma^2}$ as with all log-normal distributions so $E[Y(t)^2] = e^{2\mu+2\sigma^2}$.
You want  $E[Y(t)^2]+6E[Y(t)]+9$ 
