For time 0 < t < 8, people arrive at a venue for an outdoor concert at a rate modeled by the function A defined by A (t) = 0.3 sm(1.9i) + 0.3 cos(0.6i) + 1.3. For time 0 < £ < 1, no one leaves the venue, and for time 1 < < 8, people leave the venue at a rate modeled by the function L defined by L (£) = 0.2 cos(1.9£) + 0.2 sin£ + 0.8. Both A (£) and L (£) are measured in hundreds of people per hour, and £ is measured in hours. The number of people at the venue, in hundreds, at time hours is given by P (£). (a) At time £ = 2, there are 6 hundred people at the venue. Write an equation for the locally linearapproximation of P at £ = 2, and use it to approximate the number of people at the venue at time£ = 2.5.