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

Emeli Hagan 2021-02-05 Answered
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
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Expert Answer

Brittany Patton
Answered 2021-02-06 Author has 100 answers

Given model is y=192(0.96)t
Rewrite the above model as y=192(10.04)t
Compare the model y=192(10.04)t with it's standard form
y=a(1r)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=log0.96(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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