Right t-exact functors from left-bounded categories

Exercise 6.3.35. Let \(C\) and \(D\) be stable \(\infty \)-categories with t-structure, and assume that \(C\) is left bounded. Show that the restriction functor \[ \Fun ^{t-\rex }(C,D) \iso \Fun ^{\rex }(C_{\geq 0}, D_{\geq 0}) \] provides an equivalence between right t-exact functors \(F\colon C \to D\) and right exact functors \(C_{\geq 0} \to D_{\geq 0}\).