Question

A new smartphone can be purchased for $840. The phone’s value has a half-life of 23 months and can be modelled by the function 

𝑉 = 840(0.5) 𝑡/23

Algebraically determine how long, to the nearest tenth of a month, it takes the smartphone to be worth $601

Answer 1

$V=840(0.5)^\frac {t} {23}$

Given $V=601$

$601=840(0.5)^\frac {t} {23}$

$\frac {601}{840}=(0.5)^\frac {t} {23}$

$Log(\frac {601} {840}) =\frac {t} {23} Log 0.5$

$-0.145404814=\frac {t} {23} ×-0.301029996$

$t=\frac {23×0.145404814}{0.301029996}$

$t=11.1095$

$t=11.11months$