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Hello, in this my post, I will not make calculations for you, using ICT, because I don't know what ICT is.
And, in general, it is out of my principles of tutoring to make somebodies' job, which is pressing buttons,
since it has no any relation to teaching. Making students' job, substituting students in pressing
buttons is the worst possible tutors service which I can imagine - so, I never do it.
My post is about another issue. I simply want to explain you
what your problem is about and, conceptually, what you should do with it.
If the function i(t) = 100.e((0.2t) is the growth rate, as it is written in your post,
it literally means that the population function is the integral of it, i.e. the anti-derivative of this function.
Anti-derivative of i(t) = 100.e^(0.2t) is N(t) = 500.e^(0.2t) (plus, formally, a constant).
It means that calculations in the posts of other tutors (both @josgatithmetic and @Theo) are INCORRECT and IRRELEVANT.
They are irrelevant, since they MISTAKENLY treat the given growth rate function i(t) as a population function N(t).
So, again, the calculations in their posts are not consistent with wording in your post.
This discrepancy is that fundamental danger moment which I want to point/(to warn)/(to aware) you.
Next, to answer first question, you have two options, or two ways.
First way is to calculate 10 values i(1), i(2), i(3), . . . , i(10) separately and then add all of them.
You may round each value on the way, or round the final sum
- I do not think that it makes any serious difference.
Notice that the sequence i(1), i(2), i(3), . . . , i(10) is a geometric progression,
so you can use the formula for the sum of geometric progression.
Second way is to calculate N(10) - N(0), using the population function.
To answer second question, simply calculate i(11) and round it.
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In his post, regarding my writing, @greenestamps positions himself as a person,
who can read in the head of visitors. Perhaps, he has such super-skills, but I don't.
Moreover, I am even not going to do it.
I react as I read, and I read what I see. My reaction was perfectly adequate to the posted problem.
/\/\/\/\/\/\/\/
I re-read the incoming post again. I see there this written text
"The growth rate of the number of insects per day is described by the function i(t) = 100. e^0.2t".
OK, I may assume that the person made a typo or a mistake saying "the growth rate" instead of "population",
but next he writes "per day", highlighting the idea and clearly showing that it is really "the growth rate"
and is not a typo or mistake.
So, I really do not understand why I should treat it in another way.
Only because @greenestamps wants it ?
Resume: My solution is ABSOLUTELY CORRECT * * * * *
Comment from @greenestamps is ANSOLUTELY WRONG.
