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course Mth 173
2/16 4pm
Determine the average rate at which the quadratic function y = .02 t2 + -2.4 t + 77 changes between clock times t = 32.2 and t = 32.2 + .1 sec; between clock times t = 32.2 and t = 32.2 + .01 sec; and between clock times t = 32.2 and t = 32.2 + .001 sec. At what rate do you conjecture this function will be changing at the instant t = 32.2 sec?We y = .02 t2 + -2.4 t + 77 so
if t = 32.2, y =.02*32.2^2 - 2.4*32.2 + 77 = 20.4568,
if t = 32.2 + .1 = 32.3, y =.02*32.3^2 - 2.4*32.3 + 77 = 20.3458,
if t = 32.2 + .01 = 32.21, y =.02*32.21^2 - 2.4*32.21 + 77 = 20.445682 and
if t = 32.2 + .001 = 32.201, y =.02*32.201^2 - 2.4*32.201 + 77 = 20.45568802.
The average rate at which the quadratic function y changes between clock times t = 32.2 and t = 32.2 + .1 sec is (20.3458- 20.4568) / (32.2 + .1 - 32.2) = -.111/.1 sec.
The average rate at which the quadratic function y changes between clock times t = 32.2 and t = 32.2 + 01 sec is (20.445682 - 20.4568) / (32.2 + .01 - 32.2) = -.0111/.01 sec.
The average rate at which the quadratic function y changes between clock times t = 32.2 and t = 32.2 + .001 sec is (20.45568802- 20.4568) / (32.2 + .001 - 32.2) = - .00111/.001 sec.
From above, we can guess that at instant t = 32.2, the rate this function will be changing is -1.11 / sec.
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