course Mth 271
If the function y = .019 t2 + -2.1 t + 80 represents depth y vs. clock time t, then what is the average rate of depth change between clock time t = 15.1 and clock time t = 30.2? What is the rate of depth change at the clock time halfway between t = 15.1 and t = 30.2?
The rate of change would be -1.239
What function represents the rate r of depth change at clock time t? What is the clock time halfway between t = 15.1 and t = 30.2, and what is the rate of depth change at this instant?
Y=.019t^2=-2.1t+80
The half life would be 22.65
The problem didn't ask for half-life, which isn't a concept that applies to this situation.
If the function r(t) = .017 t + -1.5 represents the rate at which depth is changing at clock time t, then how much depth change will there be between clock times t = 15.1 and t = 30.2?
• What function represents the depth?
• Y’= .038t+-2.1
• What would this function be if it was known that at clock time t = 0 the depth is 90 ?
Not sure of what this last point is asking or how to do it.
If the rate function, i.e., the function which describes the rate of change of y with respect to t is
y ' (t) = m t + b,
then the depth function is
y(t) = 1/2mt^2 + bt + c,
where c is an arbitrary constant.
You're given the rate function, so you have to identify m (which is the coefficient of t) and b.
The Modeling Project describes this process, in the same place you saw the y(t) = 1/2mt^2 + bt + c expression.
Except for the designation of the function (y(t), not y ' (t)) and the existence of the arbitrary constant c, you've done this right.
You still need to evaluate the contant c, using the knowledge that when t = 0 we have y = 90.
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