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\textbf{Math 220 (section AD?) \hfill Quiz 6 \hfill Fall 2016} \\
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\textbf{Name}\ \rule{4in}{0.4pt} \hfill
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$\bullet$ You have 20 minutes \hfill $\bullet$ No calculators \hfill $\bullet$ Show sufficient work
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\item (4 points) The height of a remote-controlled drone in feet above ground for $t \geq 0 $ seconds is given by the following function.
$$h(t) = 3t^{2}e^{-t/10}$$
What is the maximum height obtained by the drone?
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\item (3 points) There is a launch site of a hot-air balloon on the ground $20$ meters away from an observor. The balloon rises vertically at a constant rate of $2$ meters per second. How quickly is the angle of elevation of the balloon increasing $5$ seconds after its launch?
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\item (3 points) Determine the formula for a function whose graph passes through the point $(6, e^{10})$ and has the property that for each point on the curve, the slope of the curve is equal to one half its $y$-coordinate.
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