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

Emeli Hagan

Answered question

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

Answer & Explanation

Brittany Patton

Brittany Patton

Skilled2021-02-06Added 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)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?