The Food and Drug Administration labels suntan products

Chapter 3, Problem 3.3.13

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The Food and Drug Administration labels suntan products with a sun protection factor (SPF) typically between 2 and 45. Multiplying the SPF by the number of unprotected minutes you can stay in the sun without burning, you are supposed to get the increased number of safe sun minutes. For example, if you can stay unprotected in the sun for 30 minutes without burning and you apply a product with a SPF of 10, then supposedly you can sun safely for 30 10 300 minutes or 5 hours. Assume that you can stay unprotected in the sun for 20 minutes without burning. a. Write an equation that gives the maximum safe sun time T as a function of S, the sun protection factor (SPF). b. Graph your equation. What is a suggested domain for S? c. Write an inequality that suggests times that would be unsafe to stay out in the sun. d. Shade in and label regions on the graph that indicate safe and unsafe regions. (Use two different shadings and remember to include boundaries.) e. How would the graph change if you could stay unprotected in the sun for 40 minutes? Note that you should be cautious about spending too much time in the sun. Factors such as water, wind, and sun intensity can diminish the effect of SPF products.