9. The time gap between lightning and thunder occurs because the sound travels more slowly than light. This table gives the speed of sound in air at various temperatures. Temperature (C) о 10 20 30 Velocity (m/s) 332 338 344 350 a) Create a scatter plot for the data. b) Determine the equation of the line of best fit. c) What does the rate of change represent in this context? d) Predict the speed of the sound at these temperatures using the graph. 50 c) Use your equation for the line of best fit to calculate the speed of sound at -3°C. 10. Ryan planted 2000 acres of soybeans across from the school. During the last fire drill, the beans were harvested using a combine. Ryan has kept a graph of the number of acres left for him to harvest. a. Describe the relationship between the area remaining and the # of days. Ryan's Harvest b. Use the graph to estimate the area remaining after three days. c. By how much does the area remaining decrease after each day of harvest? d. Consider the rate of change of area remaining with respect to the number of days. What are suitable units for this rate of change? Area Remair 2000 1500 1000: 500 246810 Day e. Is the rate of change of area remaining with respect to the number of days increasing, constant or decreasing? Give a reason for your answer £ Predict the number of days required to complete the harvest. Show your work. 11. The table shows the average amount households spend annually on utilities in a particular community. Calculate the finite differences (first and second differences) and the ratios. Year 2000 Average Amount ($) 6214.00 2001 6648.98 2002 7083.92 2003 7518.89 2004 7953.90 First Difference Second Difference Ratios a) Which model appears most suitable: linear, quadratic, exponential, or none of these? 3 3₁₂-mx+b STATISTICS 7=1 RESIDUALS plot Xb) Desmo produced the data to the left for this table (assuming 2000 to be year 0). Write the following equations: Linear: PARAMETERS m=434.971 b=6214 Exponential: y₁-ax² + bx₁ + c STATISTICS RESIDUALS plot PARAMETERS a=0.00642857 b=434.945 c=6214.01 X Quadratic: c) Use the model you think is best to calculate the average amount spent on utilities in 1995. y₁-a(b)* Log Mode STATISTICS R²=0.9987 RESIDUALS PARAMETERS a=6242.62 b=1.06326