The position of an object at time t is given by s (t). Find the instantaneous velocity at the indicated value of t.

s (t) = 4at^2 + 7 at t = 4

If the position is given by s (t) = 4at^2 + 7

(by which I assume you mean s (t) = 4*a*t^2 + 7)

then the velocity is given by the derivative ds/dt, which is 4*a*2*t.

Now let t = 4: (ds/dt) (4) = 4*a*2^4 = 4*a*16 = 64a (answer)

S (t) = 4at^2 + 7

s' (t) = v = 8at

so velocity at t = 4 = 8a*4 = 32a