limits on Solarized Sublime Sekai
https://vincenttam.gitlab.io/tags/limits/
Recent content in limits on Solarized Sublime SekaiHugo -- gohugo.iosere@live.hk (Vincent Tam)sere@live.hk (Vincent Tam)Mon, 19 Sep 2022 14:23:17 +0200Exponential Function Product Rule
https://vincenttam.gitlab.io/post/2022-09-19-exponential-function-product-rule/
Mon, 19 Sep 2022 14:23:17 +0200sere@live.hk (Vincent Tam)https://vincenttam.gitlab.io/post/2022-09-19-exponential-function-product-rule/Motivation from compound interest Increase the number of times that the interest is compounded each year ($n$), so as to increase the final amount of money ($A$)
$$A = P \left(1 + \frac{r}{n}\right)^{nt}.$$ $t$ and $r$ are the number of years and the interest rate per annum.
As $n$ becomes large, we can approximate the amount by
$$A = P e^{rt}.$$ The value of $A$ in the above formula is the amount compounded continuously.