Question 87048
{{{d=750e^(-0.0005x)}}} Start with the given equation


{{{200=750e^(-0.0005x)}}} Plug in {{{d=200}}}


{{{200/750=e^(-0.0005x)}}} Divide both sides by 750


{{{4/15=e^(-0.0005x)}}} Reduce


{{{ln(4/15)=-0.0005x}}} Take the natural log of both sides. This undoes the base of "e"


{{{-1.322=-0.0005x}}} Evaluate the natural log of {{{4/15}}}


{{{-1.322/-0.0005=x}}} Divide both sides by -0.0005


So our answer is 


{{{x=2644}}}