Question

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

Exponential growth and decay
ANSWERED
asked 2021-02-05
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 model for the value of a home represents exponential _____. (Enter growth or decay in the blank.)
2. The annual percent increase or decrease in the value of the home is ______ %. (Enter the correct number in the blank.)
3. The value of the home will be approximately $161,000 in the year

Answers (1)

2021-02-06

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)

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