[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:
- [tex]\bold{y=Ce^{kt}}[/tex]
- [tex]\bold{(0, \dfrac{6}{7} )}[/tex]
[tex]\small\leadsto\bold{Substitute:}[/tex]
[tex]\longrightarrow\sf{ \dfrac{6}{7}= Ce^{k*0}}[/tex]
[tex]\longrightarrow\sf{\dfrac{6}{7}= C*e^0}[/tex]
[tex]\longrightarrow\sf{e^0=1}[/tex]
[tex]\therefore\sf{C= \dfrac{6}{7} }[/tex]
[tex]\therefore\sf{5=Ce^{k*5}}[/tex]
[tex]\\[/tex]
[tex] \bold{Solve \: to \: find \: k:}[/tex]
[tex]\longrightarrow\sf{5 = \dfrac{6}{7} *e^{k5}}[/tex]
[tex]\longrightarrow\sf{ \dfrac{7*5}{6} *e^{5k}}[/tex]
[tex]\longrightarrow\sf{In=( \dfrac{35}{6} ) = 5k}[/tex]
[tex]\longrightarrow\sf{1.76=5k}[/tex]
[tex]\longrightarrow\sf{k=\dfrac{1.76}{5} = 0.352}[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\large\sf{\boxed{\sf \dfrac{6}{7}= e^{0.352*t}}}[/tex]
