Two ways to write 15-b
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The domain is the set of allowed inputs, in this case t values. The smallest t value allowed is t = 0. The largest is t = 165. So that's why the domain is 
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The range is
since H = 0 is the smallest output of the function and H = 40,000 is the largest output. Like the domain, the range is the set of possible outputs of a function.
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The range is