### Engl 3550 Physics Portion Assignment 9 - Answers

In a recent article it is claimed that a single CT scan would increase the chances of dying from cancer by 1 in 2,000. When compared to the overall risk of dying from cancer (about 400 in 2,000, or 20%) this doesn't seem like a large risk. But . . . . . .

1. Take the data you found from assignment 1 and estimate the extra number of cancer deaths in the US per year.
1. The percentage increase is 0.25%, from 400 to 401 cases per year per 2,000 people. 1/400 = 0.25%. Note that the 2000 is basically irrelevant, we could equally well have used a population size of 2 million. In the case the increase would have been from 400,000 in 2 million to 401,000 in 2 million, again an increase of 0.25%.

Since there are approximately 600,000 cancer deaths per year, then the increase should be 0.25% * 600,000 or about 1,500 per year.

2. If the average life span of a US citizen is 80 years how many total extra deaths might be expected?
1. Assuming that nether the population nor the death rate changes over time, and ignoring the relatively few people who have more than one CT scan, then the extra number of deaths should be about 1,500 per year * 80 years or 120,000 total number of people who die from cancer directly as result of CT scans.

3. Do you think that this number of extra deaths is acceptable for the economic benefits that are being projected?
1. You have to bear in mind why CT scans are used. As a diagnostic tool they can indicate the need for treatment of existing conditions, which in turn can save lives. If the number of lives saved is far greater than the number above then the benefits outweigh the risk, and we might conclude that the extra number of deaths is indeed acceptable.

You can make the same argument about any "dangerous" activity, such as driving, chemotherapy, and nuclear power. If nuclear power were to be shown to cause 1,000 deaths per year, but could "save" 5,000 lives per year by replacing fossil fuel power plants (a major cause of air pollution and therefore deaths) then you might also conclude that the risk is worth it relative to the benefits.

It all comes down to the numbers, a topic we will return to in the spring.