Question

a calf weighs wo pounds at birth gains wight at the rat dw/dt= 1200-w where w is wight in pounds and t is time in years

Answer 1

$\dfrac{\mathrm dw}{\mathrm dt}=1200-w$
$\dfrac{\mathrm dw}{w-1200}=-\mathrm dt$
$\displaystyle\int\dfrac{\mathrm dw}{w-1200}=-\int\mathrm dt$
$\ln|w-1200|=-t+C$
$e^{\ln|w-1200|}=e^{-t+C}$
$w-1200=Ce^{-t}$
$w=1200+Ce^{-t}$