Older women experienced menopause. Their body doesn't function as it used to.

.. More prone to hormonal imbalances ..thus more prone to hormone induced cancers.

Basically there are two different reasons:

1) solid tumors increase with age. Accumulation of mutations may be one of the cause like in colon cancer and oxidative stress to which tissues have been exposed for many years.

2) breast cancer is highly dependent on hormonal influence. Many years of estrogenic stimulation may increase mutational risk.

As a proof of concept we can see that hereditary cancer like BRCA 1 or 2 appear at a younger age.

Maybe more women want to be screened for breast cancer after the age of 30.