I know that in general exact-by-exact extensions of $C^*$-algebras need not be exact. Is it true that, if we have a short exact sequence of $C^*$-algebras

$$0 \to I \to A \to B \to 0$$

such that $I$ is exact and $B$ is nuclear, then $A$ is exact?

If it is true, could you give a reference of the result? If it is false, could you give a counterexample?

Thanks in advance.