Question 1207489
your equation appears to be:


f(t) = 100 * e ^ (.2 * t).


when t = 0, the formula becomes f(t) = 100 * e ^ (0).


since e ^ (.2 * 0) = 1, then f(t) = 100 when t = 0.


it appears that, at t = 0, you have 100 insects.


when t = 10, you have 100 * e ^ (.2 * 10) = 738.9056099 insects.


that is 638.9056099 more than when you started.


that's your growth.


when t = 11, you will have 738.9056099 * e ^ (.2 * (11 - 10) = 738.9056099 * e ^ (.2 * 1) = 902.5013499 insects.


your growth is 902.5013499 minus 738.9056099 = 163.59574 insects in 1 additional day from day 10 to day 11.


this equation can be graphed.


it looks like this.


<img src = "http://theo.x10hosting.com/2024/060901.jpg">


since the number of insects has to be an integer, then you need to round your results.


your choice is to round your final results only, or to round all intermediate results as well.


an argument can be made that you would need to round all intermediate results, since the number of insects has to be an integer every time you take a tally.


the spreadsheet below shows the results of not rounding, rounding after all calculations have been performed, rounding down only, rounding up only, or rounding to the nearest integer.


you just need to decide which rounding option is appropriate for the problem you are working n.


<img src = "http://theo.x10hosting.com/2024/060902.jpg">