The value of a home y (in thousands of dollars) can be approximated by the model, y= 192 (0.96)^t where t is the number of years since 2010. 1. The mo

Given model is $y=192(0.96{)}^t$
Rewrite the above model as $y=192(1-0.04{)}^t$
Compare the model $y=192(1-0.04{)}^t$ with it's standard form
$y=a(1-r{)}^t$ and obtain that r=0.04 and a=192
Now substitute y=161 and solve for t as follows.
$y=192(0.96{)}^t$
$161=192(0.96{)}^t$
$(0.96{)}^t=(161)/(192)$
$t={\log }_{0.96}(161/192)$
t=4.3136
Thus,
1.The model for the value of a home represents exponential decay.
2.The annual percent increase or decrease in the value of the home is 4%.
3.The value of the home will be approximately $161,000 in the year 2014.
(2010+4=2014)