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A graphing calculator is recommended. A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is 0.17. It can be shown that the downward velocity of the sky diver at time t is given by v(t) = 160(1e-0.17t) where t is measured in seconds (s) and v(t) is measured in feet per second (ft/s). (a) Find the initial velocity of the sky diver. ft/s (b) Find the velocity after 3 s and after 18 s. (Round your answers to one decimal place.) after 3 s ft/s ft/s after 18 s (c) Draw a graph of the velocity function v(t).
v(t) 200 150 100 O 50 v(t) 200 150 100 10 50 20 10 30 20 40 t v(t) 200 150 v(t) 2000 150 AL 100 50 30 40 100 O 50 10 20 10 30 20 30 40 40 t (d) The maximum velocity of a falling object with wind resistance is called its terminal velocity. From the graph in part (c) find the terminal velocity of this sky diver. (Round your answer to the nearest whole number.) ft/s
A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t) = 13e-0.011t where m(t) is measured in kilograms. (a) Find the mass at time t = 0. kg (b) How much of the mass remains after 48 days? (Round your answer to one decimal place.) kg Need Help? Read It Watch It
Graph the function, not by plotting points, but by starting from the graph of y = ex in the figure below. y = e-x - 2 -4 y y = 3/ y = 2x J y = ex -2 y 4 2 N 2 X 4 X -4 -2 y 4 2 2 4
O range -4 -2 State the asymptote. 4 2 2 4 X O State the domain and range. (Enter your answers using interval notation.) domain -4 -2 y 4 2 4 X