Answer Happy

The average typing speed S (in words per minute) of a typing student after t weeks of lessons is shown in the table. t 5 10 15 20 25 30 S 39 55 80 91 94 96 A model for the data is 100r² 0 < t < 30. 65+12 (a) Use a graphing utility to plot the data and graph the model.. S= 100 80 60 40 20 5 10 5 15 100 80 r 60 40 201 10 concave downwards 20 15 25 20 25 30 30 80 GO 40 20 60 40 20 5 (c) What is the sign of the first derivative for 0 < t < 30? S'(t) < 0 for 0 < t < 30. S'(t) > 0 for 0 < t < 30. 5 10 10 15 15. 20 25 20 25 30 (b) Use the second derivative to determine the concavity of S. Compare the result with the graph in part (a). (Enter your answers using interval notation. Round your answers to two decimal places.) concave upwards 30

100 80 60 40 20 5 10 15 20 25 40 20 3 10 15 (c) What is the sign of the first derivative for 0 < t < 30? S'(t) < 0 for 0 < t < 30. S'(t) > 0 for 0 < t < 30. 20 25 30 (b) Use the second derivative to determine the concavity of S. Compare the result with the graph in part (a). (Enter your answers using interval notation. Round your answers to two decimal places.) concave upwards concave downwards By combining this information with the concavity of the model, what inferences can be made about the typing speed as t increases? As t increases, the speed increases, but at a slower rate. As t increases, the speed increases at a constant rate. As t increases, the speed decreases, but at a slower rate. As t increases, the speed remains constant. As t increases, the speed decreases at a constant rate.