A home is valued at $236,500 in 2012. In 2017, the home is worth $305,700. Assume the home's value is increasing exponentially. a. Construct a function V(t) which models the value of the home as a function of years since 2012. b. If the model holds, what year will the home value be worth $400,000?

Jaden Easton

Jaden Easton

Answered question

2020-11-08

A home is valued at $236,500 in 2012. In 2017, the home is worth $305,700. Assume the homes

Answer & Explanation

wheezym

wheezym

Skilled2020-11-09Added 103 answers

Consider the following exponential function of value of the home:
V(t)=abt
Where,
V(t)=Value of home after t years
t=number of years from 2012
a and b are constants
In 2012, value of home is $236,500
ab0=236500
a=236500
In 2017, value of home is $305,700
t=20172012
=5
236500×b5=305700
b5=305700236500
b5=1.2926
b=5{1.2926}
b=1.05267
Hence, the exponential function is V(t)=236500×(1.05267)t=400000
(1.05267)t=400000236500
(1.05267)t=1.691332
Take logarithm on both sides of the equation:
t×log(1.05267)=log(1.691332)
t=log(1.691332)log(1.05267)
=0.2282290.02229
=10.23
10
Hence, after 10 years value of home will become $400,000.

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