Section 8.6Comparing Linear, Exponential, andQuadratic Functions 46730. MODELING WITH MATHEMATICS The table shows the breathing rates y (in liters of air per minute) of a cyclist traveling at different speeds x (in miles perhour).Speed, x 2021222324Breathing rate, y51.457.163.370.378.0 a. Plot the points. Let the speed x represent the independent variable. Then determine the type offunction that best represents this situation. b. Write a function that models the data. c. Find the breathing rate of a cyclist traveling 18miles per hour. Round your answer to the nearest tenth. 31. ANALYZING RATES OF CHANGE The function f (t) 16t2 + 48t + 3 represents the height (in feet) of a volleyball t seconds after it is hit into the air. a. Copy and complete the table.t00.511.522.53f (t)b. Plot the ordered pairs and draw a smooth curve through the points.c. Describe where the function is increasing and decreasing.d. Find the average rate of change for each 0.5-second interval in the table. What do you notice about the average rates of change when the function is increasing? decreasing?32. ANALYZING RELATIONSHIPS The population of Town A in 1970 was 3000. The population of TownA increased by 20% every decade. Let x represent the number of decades since 1970. The graph shows the population of Town B. (See Example 4.)a. Compare the populations of the towns by calculating and interpreting the average rates of change from 1990 to2010. b. Predict which town will have a greater population after 2020. Explain.33. ANALYZING RELATIONSHIPS Three organizations are collecting donations for a cause. Organization A begins with one donation, and the number of donations quadruples each hour. The table shows the numbers of donations collected by Organization B. The graph shows the numbers of donations collected by Organization C.Time (hours), tNumber of donations, y001428312416520624a. What type of function represents the numbers of donations collected by Organization A? B? C?b. Find the average rates of change of each function for each 1-hour interval from t 0 to t 6. c. For which function does the average rate of change increase most quickly? What does this tell you about the numbers of donations collected by the three organizations? 34. COMPARING FUNCTIONS The room expenses for two different resorts are shown. (See Example 5.)Vacations available up to 14 nights. Each additional night is a 10% increase in price from the previous package. a. For what length of vacation does each resort cost about the same? b. Suppose Blue Water Resort charges $1450 for the rst three nights and $105 for each additional night. Would Sea Breeze Resort ever be more expensive than Blue Water Resort? Explain. c. Suppose Sea Breeze Resort charges $1200 for the rst three nights. The charge increases 10% for each additional night. Would Blue Water Resort ever be more expensive than Sea Breeze Resort? Explain.ty804001601200624(2, 16)(3, 36)(0, 0)(1, 4)(4, 64)Time (hours)Number of donationsOrganization C(6, 144)(5, 100)