Math 229 Lab 12: Sections 12.3, 12.4 & 12.5 Name: Use good notation and show all of your work. Write solutions to word problems in a sentence. 1. Assume that the total revenue (in dollars) from the sale of x TV is given by R(x) = 24(22 + 2) 2/3. (a) Find the marginal revenue function. (b) Find the marginal revenue when (c) Find the marginal revenue when 100 TVs are sold. 200 TVs are sold. (d) Find the average revenue function. (e) Find the marginal average revenue function. 2. The sales of a new personal computer (in thousands) are given by S(t) = 100 - 90e-0.3t, where t represents the times in years. (a) Find the rate of change of sales. (b) Find the rate of change of sales (c) Find the rate of change of sales after 1 year. after 5 years. (d) What is happening to the rate of change of sales as time goes on? Page 1Math 229 Lab 12: Sections 12.3, 12.4 & 12.5 Name: 3. After the introduction of a new product for UV protective clothing, the percent of the public that is aware of the product is approximated by A(t) = 10t22-, where t is the time in months. (a) Find the rate of change of the percent of (b) Find the rate of change of the percent of the the public that is aware of the product public that is aware of the product after 2 after 2 months. months. (c) Notice that the answer to part (a) is positive and the answer to part (b) is negative. What does this tell you about how public awareness of the product has changed? 50 4. Suppose the demand function for q units of Kittenballs is p = 100 + Ing' 9 > 1, where p is in dollars. (a) Find the marginal revenue function. (b) Approximate the revenue from one more unit when 8 units are sold. (c) How might a manger use the information from part (b)? Page 2