Let y(x)=C eʳ x, where C( neq 0) and r are real numbers, be a solution to a differential equation. Suppose we cannot determine r exactly but can only approximate it by tilder. Let tildey(x):=C e^ tilder x and consider the error |y(x)- tildey(x)|.

**(a)** If r and tilder are positive, r neq tilder, show that the error grows exponentially large as x approaches + infty.
**(b)** If r and tilder are negative, r neq tilder, show that the error goes to zero exponentially as x approaches + infty.