# Math Help - logarithm/exponential word problem

1. ## logarithm/exponential word problem

The value V of a certain automobile that is t years old can be modeled by
$V(t)=14,044(0.8)^t$.
According to the model, when will the car be worth:
(a) $8000? (b)$7000?
(c) $1000? Answers: (a) 2.5 years (b) 3.1 years (c) 11.8 years It says I need to rewrite the problem in logarithmic form, how would I do this? $log 8000 = log 14044(.8)^t$? 2. Originally Posted by desiderius1 The value V of a certain automobile that is t years old can be modeled by $V(t)=14,044(0.8)^t$. According to the model, when will the car be worth: (a)$8000?
(b) $7000? (c)$1000?

(a) 2.5 years
(b) 3.1 years
(c) 11.8 years

It says I need to rewrite the problem in logarithmic form, how would I do this?
$log 8000 = log 14044(.8)^t$?
$V=14044(0.8)^t$
$\frac{V}{14044}= (0.8)^t$
$\log_{0.8}\frac{V}{14044}= t$
$t= \log_{0.8}\frac{V}{14044}$