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: 32: ca:2 +bx+c Power: yzam\" Exponential: y: a-b" Logarithm: y=a+b1nx 1. A house is bought in an up-and-coming Texas neighborhood. The table below shows the value of the house, V(t), after owning the house for tyears. r in ' V(t) value of house years 2 $150,000 4 $225,000 6 s 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) ? (:1. Find a particular equation for V(r) and verify that all of the V(t) 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. 3. Below is a table relating altitude, h, and atmospheric pressure P(h). Altitude above sea level Atmospheric (km) Pressure (kPa) 2 80 4 64 6 51 .2 8 40.96 a. Determine the atmospheric pressure at 10 km above sea level. _ I _ _ 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? 0. Why can't you use the pattern to find P(5)? d. Find a particular equation for P(h) and verify that all of the P(h) values in the given table satisfy the equation. (Leave your equation exact.) e. Evaluate P(5). f. At what altitude will the atmospheric pressure reach 25 kPa? Give both, the exact (without calculator) and approximate (with calculator) answers