HW 3.4.1: Applications of Function Patterns Use your knowledge of function patterns to answer the questions below. At this point in the year, you have the skills to determine the regression function for linear and exponential without using a calculator. However, if the function modeled is quadratic, power, or logarithmic, a calculator is needed. Linear: y = ax+b Quadratic: y= ax + bx+ c Power: y = a.x Exponential: y= a. b* Logarithm: y=a+blnx 1. A house is bought in an up and coming Texas neighborhood. The table below shows the value of the house, V(), after owning the house for t years. t in V(t) value of house years 2 $150,000 4 $225,000 6 $337,500 8 $506,250 a. Determine the price of the home after 12 years. b. Use the function properties that you learned previously to make a conjecture as to the type of function that models the given data. What type of function models this pattern? c. Why can't you use the pattern to find V(15) ? d. Find a particular equation for V() and verify that all of the V() values in the given table satisfy the equation. (Leave your equation exact.) e. Evaluate V(15). f. In what year will the house be worth 5 million dollars? Give both, the exact (without calculator) and approximate (with calculator) answers.2. A Cessna airplane is taking off on a runway. You start recording the velocity as a function of time slightly after it has started. Below is a table of your results. . a. Determine the velocity of the plane after 43 seconds. in. Use the function propenies that you Ieamed previously to make a conjecture as to the type of function that models the given data. What type of function models this pattern? c. Why cant you use the pattern to find was}? d. Find a particular equation for V0!) and verify that all of the wt} values in the given table satisfy the equation. e. Evaluate HIE). f. How long will it take the plane to reach 790 mph? Give both, the exact {without calculator} and approximate {with calculator} answers