I've been struggling with this one all day, and I was wondering if someone can give me a hand with the proof. I'm not even sure if the group in question is finitely generated, so I would appreciate if anyone will tell me otherwise as well. remark For infinite topological groups, I write $G$ is f...

The amount of fish in the main pool increases every month by 5%. Today, we have 6 tonnes of fish in the pool. In how many years will there be 6.6 tonnes of fish in the pool? So I can solve it like this: mt = 6.6 m0 = 6 q = 1 + 5/100 = 1.05 t = ? 6.6 = 6 * 1.05 ^ t 6.6 / 6 = 1.1 1.1 = 1.05^...

I have a textbook question that asks to use L'Hopital to show which of the two functions: $e^{0.1 x}$ vs $x^{10}$ is dominant as $x \to \infty$. That is, using: $$\lim_{x \to \infty} \left( \frac {x^ {10} } {e^{0.1 x}} \right) = \lim_{x \to \infty} \left( \frac {10x^ 9 } {0.1e^{0.1 x}} \right) ...

So if you are given two different numbers to determine a growth rate, do you use to largest number compared to the value when x=0. For example the problem I am working on is: Your grandfather purchased a house for $45,000 in 1952 and it has increased in value according to a function y = v(x), whe...

I know that the compound interest formula for the interest compounded annually is given by $$A=P(1+r)^t$$ I know the intuition behind it. But why the compound interest formula for the interest coumpounded n time per year is: $$A=P\left(1+\frac{r}{n}\right)^{nt}$$ What's the intuition behind it a...

For certain species of organisms, the effective growth rate $\ N' / N $ is highest at intermediate N. This is called the Allee effect. For example, imagine that it is too hard to find mates when N is very small, and there is too much competition for food and other resources when N is large. ...

the problem i have is as following, which i would like a solution to I am a tomato seller Everyday i sell tomatoes. I also have a demand forecast for tomatoes required everyday countrywide. Im trying to equate the number of tomatoes i sell everyday to the demand forecast. This is fine and i can ...

I've been struggling with this one all day, and I was wondering if someone can give me a hand with the proof. I'm not even sure if the group in question is finitely generated, so I would appreciate if anyone will tell me otherwise as well. remark For infinite topological groups, I write $G$ is f...