The Sixth Gate

After walking through the fifth gate, your computer informs you that more than half of the gates have been

crossed. "Only $4$ left", you conclude. "Computer, what is this gate's riddle?"

Your computer responds:

For the function, $f(t)=\frac{1}{a}(2t^3-15t^2+45{)}^{49},$ find the value of a that would make the slope of the

tangent line $-196$ at $t=2.$

$a=$