Question 1192941


{{{200=400e^(-0.0052x)}}}.........take natural log of both sides

{{{ln(200)=ln(400e^(-0.0052x))}}}

{{{ln(200)=ln(400)+ln(e^(-0.0052x))}}}

{{{ln(2*10^2)-ln(4*10^2)=(-0.0052x)ln(e)}}}

{{{(-0.0052x)ln(e)=ln(2)+ln(10^2)-(ln(2^2)+ln(10^2))}}}.......{{{ln(e)=1}}}

{{{-0.0052x=ln(2)+2ln(10)-(2ln(2)+2ln(10))}}}

{{{-0.0052x=ln(2)+2ln(10)-2ln(2)-2ln(10)}}}......simplify

{{{-0.0052x=-ln(2)}}}

{{{x=-ln(2)/-0.0052}}}

{{{x=ln(2)/0.0052}}}

{{{x=133.2975347230664}}}

{{{x=133.30}}}