Word problem about function

[salma17]

Someone please help me!
The value of U.S. trade with China from 1994 through 2004 can be approximated by
C(t)= 3t^2-7t+50 billion dollars where t is measured in years since 1994.

6) Find C(4):
a) 98
b) 56
c) 38
d) 50
e) None of the above.

7) Which of the following statements is the best interpretation of C(4)?
a) The value of U.S. trade with China in billions of dollars.
b) The value of U.S. trade with China in billions of dollars in 1994.
c) The value of U.S. trade with China in billions of dollars in 1998.
d)The amount that the value of U.S. trade with China was increasing per year in
1994.
e)The amount that the value of U.S. trade with China was increasing per year in
1998.

8) What is the average rate of change of the function between 1996 and 1998?
a)48
b)22
c)17
d)11
e)5

9) Which of the following statements is the best interpretation the answer to problem number 8?
a)The value of U.S. trade with China in billions of dollars.
b)The value of U.S. trade with China in billions of dollars in 1996.
c)The value of U.S. trade with China in billions of dollars in 1998.
d)The amount that the value of U.S. trade with China increased per year, on average, between 1996 and 1998.
e)The amount in billions of dollars that the value of U.S. trade with China increased per year, on average, between 1996 and 1998.
I got: E,B,D,A. Yes or no?
First, I plugged 4 in the function I got: C(t)=48-28+50 which is 70. so I got none of the above. as for the second part about my interpretation, that's just what i think.for 8) i plugged in 2 first so got 12-14+50 which is -48 then plugged iin 4 and got 48-28+50 which is 70 . subtract those and its 22. which is B.

 

[Ibix]

I agree with the first one.

Regarding the second, what year does t=4 correspond to?

Question 8 is ambiguous because it doesn't specify the units you should use for the rate. I would assume billions of dollars per year, though. You've just calculated the change, not the rate of change.

I don't think your last answer is right, either - think about what you are calculating in 8.

 

[salma17]

0hh right. for 8) the rate of change is found by:m = (y2-y1)/(x2-x1) so I plugged 2 in the equation first(because 1996-1994=2yrs), getting 48. so my first point is (2,48). Then I plugged in 4(1998-1994), getting 70. so my second point is (4,70). so for the rate of change i ended up with 22/2 which is 11. So it would be D.

for number 9, would it be E then?

 

[salma17]

and for 7) I got C

 

[Ibix]

Agreed on all questions now.

Questions 8 and 9 are very poor. Because 8 doesn't specify any units, any number will do. For example, the correct answer is $11bn/yr. But this can also be written as $22bn/two years, or $5.5bn/six months. Any number will do because you can hide the matching fiddle factor in the units. The kicker is that for question 9, E is correct if you use $11bn/yr, but D is correct if you express the same value in other units.

This is why units are important, kids. Rant over.