In a wind tunnel experiment, the force on a projectile due to air resistance was measured at different velocities, according to the table below. Velocity, t (100 ft/sec) 0 2 4 6 8 10 Force, p(t) (100 lb) 0 2.9 14.8 39.6 74.3 119 Follow the indicated steps to find an interpolating polynomial for these data—that is a polynomial whose graph passes through the data points given in the table. Use the function p(t) = a+at+at+at³ + a₁t² + ast³ (a) Make a plot of the data. (b) Find the system of equations with variables a,..., a, that results when the values for the velocity are substituted in for in the function above (e) Write down the augmented matrix that corresponds to the system. (d) Solve the system of equations. Determine if the system is consistent or not. If it is consistent determine if the system has a unique solution or infinitely many solutions. (e) Find the interpolating polynomial, if it exists. (f) Graph the polynomial on your plot from part (a). (g) Estimate the force on the projectile when it is traveling at 750 ft/sec. (Note the units in the table above.) (a) 0 1 2 4 8 16 32 29 1 4 16 64 256 1014 148 6 36 216 1296 777L 346 4 0 (6) p (1)=0+9,7 +9+² 10373 to 4" + ast Egli do =0 Eg 2: 64 + 4x + 803 + 16a11 +3205 = 2.4 Eg 3; 40, +1602 164403 +25694 + 102405 = 14.5 64, 1364221603 + 1296 04+ 77765-39.6 4. Eq EG 5. 10, +100024 1000 az +10000 au 110000005-114 96 811 +4492 +51203 +409644 +32,76505=74.3 d). 1 5 44 512 2096 32768 79. 10 100 1000 10000 10000 114 M100 000 0 0100 0 0 1.7125 001000-11 00000 $,6615 00010-00701 188800 1,0026. Consistent, one unique