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10.4 Outdoor Sports

10.4 Outdoor Sports
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  • Math Help

    Keep in mind as you read the solution to Example 2 that for the sake of comparison the amount of UV radiation in Seattle is assumed to be 1.

    In the solution to Example 2, note that 1.05 represents an increase of 5%. Also, because the UV radiation increases about 5% for every 1000 feet, think of 5000 feet as 5 thousand feet and 20,000 feet as 20 thousand feet. So, the solution to part (b) is 1.05 times itself 5 times, which is written as

    (1.05)5.

    The solution to part (c) is 1.05 times itself 20 times, which is written as

    (1.05)20.

    You can also think of the UV radiation increase with elevation as exponential growth (see Section 4.1), where the initial value is 1 and the rate of growth is 0.05. The model is shown below

    You can evaluate the model A = (1.05)n for n = 0, n = 5, and n = 20, which is 0 feet, 5000 feet, and 20,000 feet, respectively.

  • Consumer Suggestion

    It's important to wear sunscreen when going outside on a sunny day. Visit The Skin Cancer Foundation to learn about the different types of sunscreens and read some safety tips on how to protect yourself from the sun.

  • Checkpoint Solution
    • For the sake of comparison, assume that the amount of UV radiation in Reno is 1.
    • The difference in elevations between the peak of Mount Whitney and Reno is 14,000 - 4000 = 10,000 feet. Because the peak of Mount Whitney is 10,000 feet higher than Reno, the amount of UV radiation near the peak is

      or about 63% more than the UV radiation in Reno.

    • The difference in elevations between the peak of Mount Everest and Reno is 29,000 - 4000 = 25,000 feet. Because the peak of Mount Everest is 25,000 feet higher than Reno, the amount of UV radiation near the peak is

      or about 239% more than the UV radiation in Reno.

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