Question 575118
if you start out with 100 dollars on January and every month there is a 25% deduction of price, on what month will it take you to get a price under 25 dollars, and give an equation of how to find your answer
:
let m = month for this to be true
:
{{{100(1-.25)^m}}} = 25
{{{100(.75^m)}}} = 25
divide both side by 100
{{{.75^m}}} = {{{25/100}}}
{{{.75^m}}} = .25
use logs here
m*log(.75) = log(.25)
m = {{{log(.25)/log(.75)}}}
m = 4.82 ~ 5 months; it will less than $25 in May
;
:
Check on a calc enter: 100 * .75^5 results: $23.73