Question 1010633
{{{y=p(b)^x}}}
The dish is in some area unit.
y is how much of some area unit same unit as p.
p is initial amount of area.
x is days time
b is a factor like a rate.


<i>Bacteria in a dish double the area they cover everyday.</i>
{{{2=1*b^1}}}
{{{b=2}}}
{{{highlight_green(y=p*2^x)}}}


<i>the dish is fully covered after 25 days</i>
y is the one whole dish.  y=1 when x=25.
{{{1=p*2^25}}}
{{{p=1/2^25}}}   a very small amount of the dish.



The model may be  {{{highlight_green(y=(1/2^25)2^x)}}}.


The question is, what is x, when y=1/2 ?
{{{log((y))=log((2^-25))+x*log((2))}}}
{{{log((y))=-25*log((2))+x*log((2))}}}
{{{log((y))+25*log((2))=x*log((2))}}}
{{{(log((1/2))+25*log((2)))/log((2))=x}}}
{{{highlight(x=log((1/2))/log((2))+25)}}}


Choose the base you want for the logarithms:  Natural or Common.
Compute x.



(Day 24)