A honeybee population starts with 100 bees and increases at a rate of n'(t) bees per week. What does 100 + integrate n'(t) on [0, 15] represent?

I want to make sure I've got the right answer. The answer key doesn't provide it. It represents "The total number of bees after 15 weeks" right?

I will upload a photo of the equation soon to make it easy to understand.

Question

A honeybee population starts with 100 bees and increases at a rate of n'(t) bees per week. What does 100 + integrate n'(t) on [0, 15] represent?

I want to make sure I've got the right answer. The answer key doesn't provide it. It represents "The total number of bees after 15 weeks" right?

I will upload a photo of the equation soon to make it easy to understand.

johnt · Answer

$$100 + \int\limits_{0}^{15} n'(t)dt$$

anonymous · Answer

What this means is that the population after 15 weeks is integrated from 0 to 15. 100 is added to the change.

johnt · Answer

Wait, so would that mean "100 + the number of bees in week 1 + number in week 2 + number in week ... + number in week 15"?

anonymous · Answer

Ok, So the function n'(t) is the bees per week. So the derivative of n(t) would show the number of bees in the population in a particular week.

johnt · Answer

OK, I understand that part.

anonymous · Answer

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anonymous · Answer

n(15)-n(0) is the increase in the # of bee population during the first 15 weeks.

johnt · Answer

So, wasn't my original understanding correct? number of bees at week 15 plus 100?

anonymous · Answer

Yes.

johnt · Answer

I.e. the total bee population at week 15

johnt · Answer

ok, good. Thanks.

anonymous · Answer

It represent the total number of bees in that colony.