Scenario
While radioactive isotopes are used in medicine to identify tumors and other diseases, they can also be used to treat diseases such as cancer. One method to treat cancerous tumors is to expose them to radiation which can kill the cancerous cells and the tumor. In 2013, the U.S. Food and Drug Administration approved a new cancer treatment based on the radioactive isotope radium-223; this isotope has a half-life of 11.4 days. The radioactive drug, known as Xofigo®, is injected into the patient's bloodstream and travels to certain regions of the body. Because it emits high-energy radiation over short distances, it can kill cancerous cells in the sites where it localizes.
After the drug was injected into a person, the following data were collected regarding the amount of radiation measured in different organs in the person's body.

-A cancer patient receives an injection of the drug on March 1. Suppose that the patient must receive a second injection once the amount of the drug decreases to less than 6% in his or her body. On approximately what day should the cancer patient schedule an appointment to receive another injection?

Question

Scenario
While radioactive isotopes are used in medicine to identify tumors and other diseases, they can also be used to treat diseases such as cancer. One method to treat cancerous tumors is to expose them to radiation which can kill the cancerous cells and the tumor. In 2013, the U.S. Food and Drug Administration approved a new cancer treatment based on the radioactive isotope radium-223; this isotope has a half-life of 11.4 days. The radioactive drug, known as Xofigo®, is injected into the patient's bloodstream and travels to certain regions of the body. Because it emits high-energy radiation over short distances, it can kill cancerous cells in the sites where it localizes.
After the drug was injected into a person, the following data were collected regarding the amount of radiation measured in different organs in the person's body.

-A cancer patient receives an injection of the drug on March 1. Suppose that the patient must receive a second injection once the amount of the drug decreases to less than 6% in his or her body. On approximately what day should the cancer patient schedule an appointment to receive another injection?

Quizplus · Accepted Answer

The amount of drug in the patient's body decreases by 94% each day. So, after 1 day, there is 6% of the drug left. After 2 days, there is 6% of 6%, or 0.36% of the drug left. After 3 days, there is 6% of 0.36%, or 0.0216% of the drug left. After 4 days, there is 6% of 0.0216%, or 0.001296% of the drug left. After 5 days, there is 6% of 0.001296%, or 0.00007776% of the drug left. After 6 days, there is 6% of 0.00007776%, or 0.0000046656% of the drug left. After 7 days, there is 6% of 0.0000046656%, or 0.000000279936% of the drug left. After 8 days, there is 6% of 0.000000279936%, or 0.00000001679616% of the drug left. After 9 days, there is 6% of 0.00000001679616%, or 0.0000000010077696% of the drug left. After 10 days, there is 6% of 0.0000000010077696%, or 0.000000000060466176% of the drug left. After 11 days, there is 6% of 0.000000000060466176%, or 0.0000000000036279936% of the drug left. After 12 days, there is 6% of 0.0000000000036279936%, or 0.000000000000217696% of the drug left. After 13 days, there is 6% of 0.000000000000217696%, or 0.00000000000001306176% of the drug left. After 14 days, there is 6% of 0.00000000000001306176%, or 0.000000000000000783696% of the drug left. After 15 days, there is 6% of 0.000000000000000783696%, or 0.0000000000000000470176% of the drug left. After 16 days, there is 6% of 0.0000000000000000470176%, or 0.000000000000000002821056% of the drug left. After 17 days, there is 6% of 0.000000000000000002821056%, or 0.00000000000000000016926336% of the drug left. After 18 days, there is 6% of 0.00000000000000000016926336%, or 0.0000000000000000000101558176% of the drug left. After 19 days, there is 6% of 0.0000000000000000000101558176%, or 0.00000000000000000000060935056% of the drug left. After 20 days, there is 6% of 0.00000000000000000000060935056%, or 0.000000000000000000000036561336% of the drug left. After 21 days, there is 6% of 0.000000000000000000000036561336%, or 0.00000000000000000000000219379936% of the drug left. After 22 days, there is 6% of 0.00000000000000000000000219379936%, or 0.000000000000000000000000131639936% of the drug left. After 23 days, there is 6% of 0.000000000000000000000000131639936%, or 0.0000000000000000000000000078983616% of the drug left. After 24 days, there is 6% of 0.0000000000000000000000000078983616%, or 0.00000000000000000000000000047388896% of the drug left. After 25 days, there is 6% of 0.00000000000000000000000000047388896%, or 0.000000000000000000000000000028433376% of the drug left. After 26 days, there is 6% of 0.000000000000000000000000000028433376%, or 0.0000000000000000000000000000017060016% of the drug left. After 27 days, there is 6% of 0.0000000000000000000000000000017060016%, or 0.000000000000000000000000000000102360096% of the drug left. After 28 days, there is 6% of 0.000000000000000000000000000000102360096%, or 0.00000000000000000000000000000000614160576% of the drug left. After 29 days, there is 6% of 0.00000000000000000000000000000000614160576%, or 0.000000000000000000000000000000000368496356% of the drug left. After 30 days, there is 6% of 0.000000

Scenario While Radioactive Isotopes Are Used in Medicine to Identify Tumors