A colony of 50 bacteria doubles in size every 170 minutes. What will the population be 680 minutes from now?
2 answers:
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Remark
When you take the limit of
the odd result you get is 1. Later on you will be able to use calculus to show this. For now just take limits of sin(x)/x and make sure you are feeding radians into your calculator.
Now the only question is what is this thing doing?
If a is a constant in
then the result = a.
So that's basically all you need to know to solve your problem.
Series
Each term in the series will be
a*(sin(ax)/x) = a * [sin(ax)/x] * 1 = a * a = a^2
The series will look like this.
1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 There is a way of summing this using n notation, but you could just as easily just add the results.
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The formula for this series (if you want a sum) is n*(n+1)*(2n+1) / 6
</span>n = 10
Sum = 10*(11)(21)/6
Sum = 385
Does adding it by hand bring up 385?
When you take the limit of
Now the only question is what is this thing doing?
If a is a constant in
So that's basically all you need to know to solve your problem.
Series
Each term in the series will be
a*(sin(ax)/x) = a * [sin(ax)/x] * 1 = a * a = a^2
The series will look like this.
1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 There is a way of summing this using n notation, but you could just as easily just add the results.
<span>
The formula for this series (if you want a sum) is n*(n+1)*(2n+1) / 6
</span>n = 10
Sum = 10*(11)(21)/6
Sum = 385
Does adding it by hand bring up 385?