Quick Question on Integrals

[helen8315]

Sorry, this question is fairly simple but I feel like I'm oversimplifying it...

A population of rabbits starts off at a time of t=0 with 225 rabbits and and an increase at a rate of r(t) rabbits per month, where T is in months.

What does the expression (24 ? 36)r(t)dt represent?
I answered that this would be the net change in rabbits over months. In other words, it was the gain of rabbits, but it wouldn't show the actual amount of the rabbits, because you would have to add 225.

What does the expression ( o ? 18) r(t)dt represent?
I said that this would be the actual gain of rabbits over 18 months.

This is the one that I'm not sure on...
suppose you're told that 1/24(0 ? 24)r(t)dt =4.25, How many rabbits are in the population after 2 years?
Wouldn't it just be 225+4.25? Or am i way oversimplifying this?
I just want to make sure I'm correct in my thinking. Thanks.

 

[tkhunny]

[24,36] You have it. It is a multiplicative accumulation factor. r(t) is a rate of growth. You would need the number of rabtits at t = 24 for that to be the net change. 225 will not do and certainly not just adding it.

[0,18] Again, this is a multiplicative accumulation factor. Since you know the number of rabbits at the beginning, 225, multiply this expression by 225 to get the growth over the 1½ years.

[0,24] Careful on this one. Dividing by the length of time gives the Mean Value. This is the average rate of increase per month over the fist two years.