New here have questions

I'm going to assume by 9/6 you mean 6/9 or to be unambiguous 6 September. That was 49 days ago.

This article cautions against making predictions based on PSA increase in newly diagnosed patients, but suggests it is useful in dealing with recurrence. So my comments after this point should be taken in the context that they cannot give a reliable prognosis in your case.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3375697/

Any kind of growth fall into different mathematical categories. Cancer falls in to a class called exponential growth. The mathematics of any exponential growth can always be summarised by one figure, The doubling time.

Given two readings at different times it is possible to calculate the doubling time.

https://www.doubling-time.com/compute.php

Feeding your details into the calculator shows a doubling time of 484 days, or about a year and four months.

Now the tests are not always accurate and weren't very far apart time wise so there are possibilities of errors, until we have more information doubling time of 12 months or 18 months would be within the margins of error. Also cancer doesn't always follow mathematical rules, so it may change for better or worse.

A doubling time of less than six months is considered bad for recurrent prostate cancer.

So a doubling time of over 12 months suggests the answer to your question "is this a rapid increase?" is No.