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| rev | 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...") | Nov 17'23 at 22:31 | +490 |