The capital raised in IPOs of U$.$S$.$ companies can be modeled by

$C(t)=-2\mathrm{.}79(t-2{)}^2+34,$

where $C(t)$ represents the capital raised in IPO's of U$.$S$.$ companies in billions of dollars $t$ years since $2010.$t

$($a$)$ How much raised in IPOs of U$.$S$.$ companies in $2013?($Include units in your answer. More information.$)$

$($b$)$ In which years was $$30$ billion raised in IPO's of U$.$S$.$ companies? $($Enter your answers as a comma$-$separated list of years.$)$

$($c$)$ In which years was $$10$ billion raised in IPO's of U$.$S$.$ companies? $($Enter your answers as a comma$-$separated list of years.$)$

$($d$)$ What is the vertex of this model?

$(t,C)=(,)$

What does the vertex represent?

In the year

$,$ the capital raised in IPOS of U$.$S$.$ companies reached its