[tex]\dfrac{\mathrm dy}{\mathrm dt}=ky\iff\dfrac{\mathrm dy}y=k\,\mathrm dt[/tex]
Integrating both sides, we get
[tex]\ln|y|=kt+C[/tex]
[tex]\implies y=e^{kt+C}=e^{kt}e^C=Ce^{kt}[/tex]
When [tex]t=0[/tex], we have [tex]y=10000[/tex], so that
[tex]10000=Ce^{0k}\implies C=10000[/tex]
When [tex]t=4[/tex], we have [tex]y=8000[/tex], which means
[tex]8000=10000e^{4k}\implies k=\dfrac14\ln\dfrac{8000}{10000}\approx-0.0558[/tex]
