Revision as of 22:31, 17 November 2023 by Admin (Created page with "'''Solution: E''' <math display = "block"> \begin{align*} 2000 &= 500 \exp \left( \int_{0}^t\frac{r^2/100}{3 + r^3/150} \, dr \right) \\ 4 &= \exp \left(0.5 \int_{0}^t\frac{r^2/100}{3 + r^3/150} \, dr \right) = \exp\left[0.5\ln\left(3+\frac{r^{3}}{150}\right)\biggr|_{0}^{t} \right] \\ 4 &= \exp\left[0.5\ln \left(1+\frac{t^{3}}{450}\right)\right]=\left(1+\frac{t^{3}}{450}\right)^{\frac{1}{2}} \\ 16 &= (1 + \frac{t^3}{450}) \\ t &= 18.8988. \end{align*} </math> {{soacopy...")
Exercise
ABy Admin
Nov 17'23
Answer
Solution: E
[[math]]
\begin{align*}
2000 &= 500 \exp \left( \int_{0}^t\frac{r^2/100}{3 + r^3/150} \, dr \right) \\
4 &= \exp \left(0.5 \int_{0}^t\frac{r^2/100}{3 + r^3/150} \, dr \right) = \exp\left[0.5\ln\left(3+\frac{r^{3}}{150}\right)\biggr|_{0}^{t} \right] \\
4 &= \exp\left[0.5\ln \left(1+\frac{t^{3}}{450}\right)\right]=\left(1+\frac{t^{3}}{450}\right)^{\frac{1}{2}} \\
16 &= (1 + \frac{t^3}{450}) \\
t &= 18.8988.
\end{align*}
[[/math]]
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