Question

Easy question

Answer 1

$\dfrac{\mathrm dy}{\mathrm dt}=ky\iff\dfrac{\mathrm dy}y=k\,\mathrm dt$

Integrating both sides, we get

$\ln|y|=kt+C$
$\implies y=e^{kt+C}=e^{kt}e^C=Ce^{kt}$

When $t=0$, we have $y=10000$, so that

$10000=Ce^{0k}\implies C=10000$

When $t=4$, we have $y=8000$, which means

$8000=10000e^{4k}\implies k=\dfrac14\ln\dfrac{8000}{10000}\approx-0.0558$