Question

A company introduces a new product for which the number of units sold S is
S(t)= 200 ( 5- 9/(2+t))
where t is the time in months

(a) Find the avg. value of S(t) during the first year.
(b) During what month does S'(t) equal the avg value during the first year?

Answer 1

Either tricky question or question with really long solution.....
My method of solving will be, substituting value of t, 1 through 12 , adding all the results and dividing by 12.........Don't know if there is shortcut

Answer 2

I think you're supposed to use the mean value theorem. I mostly got it, but I don't know whether to use S(1) or s(0) in place of f(a) in the theorem.

Answer 3

(a) S(12)/12

Answer 4

my final answer for a was 5150 divided by 7. I found avg velocity by finding s(1) +s(12) all over 2. Is that wrong?

Answer 5

thatz correct, i guess

Answer 6

\[\frac{\Delta s(t)}{\Delta t}\]
would be how a physicist would find part A.
\[\frac{s(12)-s(1)}{12}\]
Of course an engineer would say:
\[\frac{s(1)+s(2)+s(3)+...+s(10)+s(11)+s(12)}{12}\]
and most mathematicians would say that there is not enough information
the rest would use Harmonic Mean just to make everyone go wtf?

Answer 7

haha I like your answer but I am none of those things, just a student. The physicist one looks the most "right" though, so I'll go with that,

Answer 8

The engineer way is Arithmetic Mean, and is generally what people mean when they ask a mean... hows that for a messed up sentence!

Answer 9

lol(: thanks for your help.

Answer 10

And you are definitely right about using Mean Value Theorem... I just don't remember how to do that O.o I know it involves some stupid limit I dont like doing.