Question 1153002
{{{y=pe^(kx)}}}

{{{1/2=1*e^(5730k)}}}

{{{1/2=e^(5730k)}}}

{{{ln(1/2)=5730k}}}

{{{-ln(2)=5730k}}}

{{{k=-ln(2)/5730}}}

{{{k=-0.000120968}}}

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{{{y=pe^(-0.000120968x)}}}
You want to find x for p=100 and y=12.


Taking logarithms of right and left sides,
and a few algebra steps:


{{{x=(ln(12)-ln(100))/(-0.000120968)}}}


{{{highlight(x=(ln(100)-ln(12))/0.000120968)}}}
Compute, and do the rounding that you need.