After working for over thirty years as a technology manager for Acme Rockets, Dottie decides that it$$s time to retire. Within a few weeks of retiring, Dottie discovers that she had been paid $20\%$ less throughout her career than male employees who did virtually the same job as her.

Two months after receiving her last paycheck from Acme, Dottie hires a lawyer and files a lawsuit against her former employer, alleging pay discrimination based on her gender.

In response, Acme claims that because the rate of pay for Dottie and other employees with jobs similar to hers was set over two years before Dottie filed suit, and because they employee more than $20$ workers who work full$-$time all year, Dottie$$s lawsuit is barred by $180-$day statute of limitations as set forth in the Age Discrimination in Employment Act.

Is Acme correct?