cancer cells secrete a chemical that circulates in the blood A measure of the amount of that chemical tells the amount of cancer cells in the body One example of this is prostate cancer The prostate is a gland that often becomes cancerous in men as they age Cancerous prostate cells secrete a prostate specific antigen or PSA A blood test for PSA is recommended for men over the age of 50 and is often used as a first warning of possible cancer One way of dealing with prostate cancer is to surgically remove the gland prostatectomy After that has been done there should be no cancer cells left and therefor no PSA found in the blood Since it s hard to get all the cancer cells and some may escape after a prostatectomy regular tests for PSA are done to detect possible presence and growth of cancer cells Another way to look for such metastatic cancer is with an MRI Magnetic Resonance Imaging or CT Computerized Tomography scan In this problem we ll estimate which method is more sensitive A spherical tumor 3 cm in diameter consisting of prostate cells may result in a PSA blood level of about 20 nanograms milliliter of blood The most common test can only detect the presence of PSA in the blood if it is greater than about 0 1 ng ml An MRI can detect a cancerous tumor down to about a diameter of 1 mm Which is a more sensitive test for the return of prostate cancer the blood test or an MRI 33 Part a To decide this estimate the diameter in mm of a tumor that would produce a PSA level just less than 0 1 ng ml 33 Part b Would a tumor that produced this undetectable amount of PSA be visible on an MRI Grade 0