If an object is dropped from an 80-metre high window, its height y above the ground at time t seconds is given by the formula y = f(t)=80-4.91². (Here we are neglecting air resistance; the graph of this function was shown in Figure 1.1.) Find the average velocity of the falling object between (a) 1 sec and 1.1 sec, (b) 1 sec and 1.01 sec, (c) 1 sec and 1.001 sec. Now use algebra to find a simple formula for the average velocity of the falling object between 1 sec and 1+At sec. Determine what happens to this average velocity as At approaches 0. That is the instantaneous velocity at time t = 1 second (it will be negative, because the object is falling). Exercise 4.1.12 The following figure shows the devastating effect the opening of a new chain coffee shop had on a 3-generation rural café in a small town. The revenue of the chain coffee shop at time t (in months) is given by f(t) million dollars, whereas the revenue of the rural café at time t is given by g(t) million dollars. Answer the following questions by giving the value of t at which the specifying event took place.