A price for a house in thousands of dollars  t  years after 2015 is given by the model  P(t)=190⋅(1.038)t Answer the following questions. 1) What was the price of the house in 2015? 2) Is the price increasing or decreasing? By how much each year? 3)Use the model to predict the price in the year 2021.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A price for a house in thousands of dollars  t  years after 2015 is given by the model 

P(t)=190⋅(1.038)t

Answer the following questions.

1) What was the price of the house in 2015?

2) Is the price increasing or decreasing? By how much each year?

3)Use the model to predict the price in the year 2021.

4) In what year the price will reach $290,000?

 

Expert Solution
Step 1

Hi, thank you for the question. Since you have posted a question with multiple subparts, as per our policy we will answer only the first three parts.

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(1)

It is given that price for a house in thousands of dollars t years after 2015 is given by the model Pt=1901.038t.

To determine price of the house in 2015, substitute t=0 in Pt=1901.038t:

P0=1901.0380=190

Thus, the price of the house in 2015 is $190 thousands.

Step 2

(2)

Substitute t=1,2,3 in Pt=1901.038t:

P1=1901.0381P1=197.22P2=1901.0382P2=204.7143P3=1901.0383P3=212.5

From above, it can be noted that the price increasing with respect to time.

Obtain the difference:

204.7143-197.22=7.5212.5-204.7143=7.7

Thus, the price is increasing by approximately 8 dollars every year.

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