Question

someone please explain this:
Explain in words what
60
0
1
( ) 100
60 0
F t dt 
 
means if () Ftis the rate, in thousands of
people per year, at which a country’s population has been growing and t is time, in years.

Answer 1

what is F(t). There an error while copying the problem. It should show this \[\frac{ 1 }{ 60-0 }\int\limits_{0}^{60}F(t)dt \approx 100\]

Answer 2

do you know the graphical significance of integration?

Answer 3

yes But I need to know what F(t) right?

Answer 4

F(t) is the function that rate at which the population of some country is growing.

the question is asking you to interpret the meaning of this:
\[\frac{ 1 }{ 60-0 }\int\limits\limits_{0}^{60}F(t)dt \approx 100\]

the question is not asking you to find the function F(t),
it is only asking you to interpret meaning of the above expression.

Answer 5

I know but what I am trying to say is , F(t) is irrelevant?

Answer 6

I suck at interpreting

Answer 7

for this question,
all we need to know is that F(t) represents rate at which the country's population is growing. We do not need to know what the actual function is.

Answer 8

so, do you know the graphical significance of integration?

Answer 9

somewhat.

Answer 10

suppose i'm driving a car
the speed of my car is given by the function v(t)
can you tell me what physical quantity we get when we do \[\int\limits v(t) dt\]
?

Answer 11

a(t)?

Answer 12

no...

Answer 13

isnit it acceleration. the derivative of acceleration is velocity.

Answer 14

the derivative of velocity is acceleration....

this is not something that needs to be memorized...
it becomes clear if you understand the meaning of derivative and integral

Answer 15

I do know them. I take higher math course than calculus. prepping for exam P.

Answer 16

Ok you are right. I got it mixed up.

Answer 17

ok :)
so can you give this another try?\[\int\limits\limits v(t) dt\]

Answer 18

@baru
Congrats on Mathlete title. :)

Answer 19

haha thank you @Will.H :D

Answer 20

Im not sre

Answer 21

i give up. this is going nowhere

Answer 22

Please note that your initial "60
0
1
( ) 100
60 0
F t dt 
  "

is practically unintelligible.

You'd get faster and better results by drawing the integral in question, as Baru attempted to do (above).

Answer 23

Here you're being asked to interpret what the given integral represents.