Hi,
If dX/dt=X/2 and X=6 million when t=5, how do you find X when t=10.
Any help would be appreciated.
Thank you!
$\dfrac{dx}{dt} = \dfrac x 2$
$\dfrac {dx}{x} = \dfrac{dt}{2}$
$\ln(x) = \dfrac t 2 + C$
$x(t) = x_0 e^{t/2},~x_0= e^C$
$x(5)=6000000 = x_0 e^{5/2}$
$x_0 =6000000e^{-5/2}$
$x(t) = 6000000e^{-5/2} e^{t/2} = 6000000e^{\frac{t-5}{2}}$