Answer:
[tex]x=e^{8t}+c[/tex]
Step-by-step explanation:
we have given x'=(24-16)x=8x
x' denotes the differenation
[tex]\frac{dx}{dt}=8x[/tex] differentiation is performed with respect to t
by variable separable method we can write
[tex]\frac{dx}{x}=8dt[/tex]
on integrating both side
[tex]lnx=8t+c[/tex]
[tex]x=e^{8t}+c[/tex] (property of log )
so the solution for x will be [tex]x=e^{8t}+c[/tex]
