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)