3. Singers Justin and Selena are playing soccer again. When Selena kicks the ball towards Justin and Justin kicks it back, the distance of the ball from Selena, in meters, \(t\) seconds after she kicks it is given by \(f(t) = e^{\frac{1}{5}t}(1 - 0.1t)\) for \(0 \le t \le 10\). Throughout this question, all your answers should be exact.
(a) Note that you can determine when Justin kicks the ball by observing when the ball changes direction. When does that happen?
(b) Check if the ball is accelerating or decelerating after 1 second and after 9 seconds.
(c) In which interval(s) is the function \(f(t)\) increasing at a decreasing rate?
