Question

The average price of a two-bedroom apartment in the uptown area of a prominent American city during the real estate boom from 1994 to 2004 can be approximated by p(t) = 0.12e0.10t million dollars (0 ≤ t ≤ 10) where t is time in years (t = 0 represents 1994). What was the average price of a two-bedroom apartment in this uptown area in 2002, and how fast was the price increasing? (Round your answers to two significant digits.)

Answer 1

Explanation:

Average price of a two bedroom apartment can be approximated by the equation,

p(t) =
`0.12e^(0.10t)`

Here, t represents the duration from year 1994.

Duration from year 1994 to year 2004 = 10 years

p(10) =
`0.12e^(0.10* 10)`

= 0.12e

= 0.3262

≈ 0.33 million

Cost of the apartment in 2004 was 0.33 million.

Let the equation to calculate the rate of increase in the price is,

p(t) =
`0.12(1+(r)/(100))^t`

Cost of the apartment after 10 years = 0.33

0.33 =
`0.12(1+(r)/(100))^(10)`

`(0.33)/(0.12)=(1+(r)/(100))^(10)`

2.75 =
`(1+(r)/(100))^(10)`

`(1+(r)/(100))=(2.75)^(0.10)`

1 +
`(r)/(100)=1.106`

`(r)/(100)=0.106`

r = 10.6%

Therefore, price of the apartment is increasing with 10.6%