Question : integration used to measure population increase


I have just read this as a ver brief example in a section in a book describing how to use integration to measure population change:

If the population of a wasp nest starts at 500 wasps and increases at a rate of W(t) wasps per week then 500 + int (from 0 to 26) W(t) dt respresents the number of wasps present after 26 weeks.

The reason why I don't get this example is because it seems like the data is discrete rather than continous. There is no such thing as the rate of change in the number of wasps at 14.5 weeks for example. Could you please explain why it is ok to integrate this


Answer : integration used to measure population increase

It is true that the number of wasps is a discrete number but the unit is amall compared with the total number so it can be treated as discrete.
When one wasp is added the percentage change is very small.
The procedure in effect averages the added wasp over the time it took to produce that wasp.
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