Solve the problem.
-If an object weighs $m$ pounds at sea level, then its weight $W$ (in pounds) at a height of $h$ miles above sea level is given approximately by $W ( h ) = m \left( \frac { 4000 } { 4000 + h } \right) ^ { 2 }$. How much will a man who weighs 165 pounds at sea level weigh on the top of a mountain which is 14,494 feet above sea level? Round to the nearest hundredth of a pound, if necessary.
A) 165 pounds
B) $164.77$ pounds
C) $7.72$ pounds
D) $165.23$ pounds

Question

Quizplus · Accepted Answer

First, convert the height from feet to miles by dividing 14,494 feet by 5,280 feet per mile, which gives approximately 2.7447 miles. Then, substitute $m = 165$ pounds and $h = 2.7447$ miles into the given formula: $W(h) = 165 \left( \frac{4000}{4000 + 2.7447} \right)^2$. Calculating this gives a weight of approximately $164.77$ pounds at the height of 14,494 feet above sea level.

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