Answer
$$f\left( t \right) = - 6t\sqrt t + 10$$
Work Step by Step
$$\eqalign{
& \frac{{dy}}{{dt}} = - 9\sqrt t \cr
& {\text{Separate the variables}} \cr
& dy = - 9\sqrt t dt \cr
& {\text{Integrate both sides}} \cr
& \int {dy} = - 9\int {{t^{1/2}}} dt \cr
& y = - 9\left( {\frac{{{t^{3/2}}}}{{3/2}}} \right) + C \cr
& y = - 6{t^{3/2}} + C{\text{ }}\left( {\bf{1}} \right) \cr
& {\text{Using the initial condition }}\left( {0,10} \right) \cr
& 10 = - 6{\left( 0 \right)^{3/2}} + C \cr
& C = 10 \cr
& {\text{Substitute }}C{\text{ into }}\left( {\bf{1}} \right) \cr
& y = - 6{t^{3/2}} + 10 \cr
& f\left( t \right) = - 6t\sqrt t + 10 \cr
& \cr
& {\text{Graph}} \cr} $$
