Can someone explain to me how they got the answer ?

Mathematics
Tutor: None Selected Time limit: 1 Day

The following table shows the number, in millions, graduating from high school in the United States, in the given year.
t = YearN = Number graduating
19852.83
19872.65
19892.47
19912.29
(b) Use functional notation to express the number of graduates in 1990.
N
(No Response)  

1990

 


Estimate its value. (Round your answer to two decimal places.)
(No Response)  

2.38

 
Oct 3rd, 2015

Hello!

I think the answer for "Use functional notation to express the number of graduates in 1990" if obvious:

N(1990).

Here N is the name of the function and 1990 is the value of the argument.

Now how to estimate this value. Of course we don't know it, actually it can be rather different.
I think they want us to suppose that the function is linear between 1989 and 1991.

( actually, because 1990 is the midpoint of [1989, 1991], the answer is also a midpoint of [N(1989), N(1991)], i.e. (2.47 + 2.29)/ 2 = 4.76/2 = 2.38 )

So we have to write equation of this line and substitute t=1990. This equation is

(t - t1)/(t2 - t1) = (N - N1)/(N2 - N1),

where t1 = 1989, t2 = 1991, N1 = 2.47 and N2 = 2.29. So

(t - 1989)/2 = (N - 2.47)/(-0.18),
N = N(t) = (-0.18)*(t - 1989)/2 + 2.47.

For t=1990 the value is

(-0.18)*1/2 + 2.47 = -0.09 + 2.47 = 2.38.


Please ask if something is unclear.
Sep 15th, 2015

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