Model radioactive decay using the notation

$t=$ time $(independent$ variable$),$

$r(t)=$ amount $of$ particular radioactive isotope

present $at$ time $t(dependent$ variable$).$

$-=$ decay rate $(parameter).$

Note that the minus sign is used so that $>0.$

$($a$)$ Using this notation, write a model for the decry of a particular ralioactive isotope.

$($b$)$ If the amount of the isotope present at $t=0$ is $r_0,$ stane the commonding initial$-$valoe problem for the model in part $($a$).$