Assignment 5 quiz

course Mth 271

I did question 9

QuestionIf the function y = .021 t2 + -1.3 t + 87 represents depth y vs. clock time t, then what is the average rate of depth change between clock time t = 7.5 and clock time t = 15? What is the rate of depth change at the clock time halfway between t = 7.5 and t = 15?

What function represents the rate r of depth change at clock time t? What is the clock time halfway between t = 7.5 and t = 15, and what is the rate of depth change at this instant?

If the function r(t) = .276 t + -1.2 represents the rate at which depth is changing at clock time t, then how much depth change will there be between clock times t = 7.5 and t = 15?

What function represents the depth?

What would this function be if it was known that at clock time t = 0 the depth is 130 ?

Answer:

y = .021 t2 + -1.3 t + 87

t = 7.5

y = .021 (7.5)^2 + -1.3 (7.5) + 87

= 1.18 - 9.73 + 87

= 78.45

t = 15

y = .021 (15)^2 + -1.3 (15) + 87

= 4.73 - 19.5 + 87

= 72.23

The half point is:

15 + 7.5/2

= 11.25

t = 11.25

y = .021 (11.25)^2 + -1.3 (11.25) + 87

= 2.66 - 14.63 + 87

= 75.03

This is the depth at the halfway point, not the requested instantaneous rate of change.

You did not calculate an average rate of change over the interval, which was also requested.

r(t) represents r of depth change

15 - 7.5 = 7.5

.276(7.5) -1.2

=.87

.276t reprsents the depth

.276 t is a term in the rate-of-depth-change function and does not directly determine the depth.

You have to find a depth function which corresponds to the given rate-of-depth-change function.

.276(130)-1.2

=34.68

You have not answered these questions correctly. You don't seem to understand the relationship between the depth function and the rate-of-depth-change function, or the calculation of an average rate of change.

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