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course Mth 173
If the function y = .022 t2 + -1.6 t + 72 represents depth y vs. clock time t, then what is the average rate of depth change between clock time t = 9.1 and clock time t = 18.2? What is the rate of depth change at the clock time halfway between t = 9.1 and t = 18.2?Y= .022(9.1^2) + -1.6 (9.1) + 72y= .022(331.24) + -1.6 (18.2) + 72
Y=1.82182 + -1.6 (9.1) +72 y= 7.28728 -29.12 + 72
Y=1.82182 - 14.56 + 72 y= 50.16728
Y= 59.26
59.26/ 50.16728 = 1.18 cm/s
Halfway= 18.2-9.1 = 9.1 so 59.26/59.26 = 1 cm/ s
What function represents the rate r of depth change at clock time t? What is the clock time halfway between t = 9.1 and t = 18.2, and what is the rate of depth change at this instant?
If the function r(t) = .176 t + -1.9 represents the rate at which depth is changing at clock time t, then how much depth change will there be between clock times t = 9.1 and t = 18.2?
• What function represents the depth?
• What would this function be if it was known that at clock time t = 0 the depth is 140 ?
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