Differentiate:
P(t)=50(2)^(t/2)
The derivative of a basic exponential when the base is not e should be one of the rules you have to know.
if y = a^u, where a > 0 and a≠ e, then
dy/dx = a^u (lna) ( du/dx)
so P'(t) = 50(2)^(t/2) (1/2) ln2
= 25 ln2 (2)^(t/2)