Suppose that the velocity v (r} {in meters per second) of a sky diver falling near the Earth's surface is given by the following exponential function, where time [ is the time after diving measured in seconds. v() =82-820 " How many seconds after diving will the sky diver's velocity be 67 meters per second? Round your answer to the nearest tenth, and do not round any intermediate computations. Dseconds ' & v (1) = 82-82e -0.18: 67 =82-8287 -0.181 To solve for t, we first isolate e -0.181 67 = 82-82e -0.18: -15 = -82e -0.18 15 -0.18: 82 We can then apply the base-e (natural) logarithm to both sides and solve. 15 In = In (e-0-18: ) 82 15 =-0.18: 82 Because In (e" ) = a 15 82 1 = -0.18 1 =9.437 ... Using the calculator Rounding our answer to the nearest tenth, we get 9.4 seconds. ANSWER 9.4 seconds