Example 2 An antiseptic spray is applied to a culture of bacteria The percent of bacteria b that are alive after t minutes is shown on the graph A secant has been drawn through the points for t 5 min and t 35 min A tangent has been drawn at the point where t 20 min a Calculate the slope of the secant Describe what the slope represents Explain the sign of the slope b Estimate the instantaneous rate of change of b with respect to t at t 20 min 100 Percent of bacteria 50 Percent of Bacteria against Time 0 5 80 20 43 35 26 20 Time minutes 40