Question 1009518
Basic model {{{y=p*e^(-kt)}}}'
y, amount after time t
p, initial amount for t=0
k, the decay constant
t, time passage


Example for the question mostly uses p=10.
(a) means, use the half-life;
(b) means, p=10,y=2, to find t for these.
(c) means, p=10, t=1000, find y.


Use algebra and skills with log and exponential functions.
{{{ln(y)=ln(pe^(-kt))}}}
{{{ln(y)=ln(p)+ln(e^(-kt))}}}
{{{ln(y)=ln(p)-kt*ln(e)}}}
{{{ln(y)=ln(p)-kt*1}}}
{{{ln(y)=ln(p)-kt}}}
{{{kt+ln(y)=ln(p)}}}
{{{kt=ln(p)-ln(y)}}}
{{{highlight_green(kt=ln(p/y))}}}-----this equation will be used in two ways.


Maybe you can do the rest of the solution on your own based on this?