#### Answer

$C(x) = 0.04(x-1970)^2+0.6(x-1970)+330+7.5~sin~2\pi x$

#### Work Step by Step

$C(x) = 0.04x^2+0.6x+330+7.5~sin~2\pi x$
We would like to define a new function $C(x)$ that is translated in the positive x-direction by 1970 units. Thus, we need to replace each $x$ in the quadratic equation part of the original function with the term $(x-1970)$.
$C(x) = 0.04(x-1970)^2+0.6(x-1970)+330+7.5~sin~2\pi x$