Jaden Easton

2020-11-08

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

wheezym

Skilled2020-11-09Added 103 answers

Consider the following exponential function of value of the home:

$V\left(t\right)=a{b}^{t}$

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

$a{b}^{0}=236500$

$a=236500$

In 2017, value of home is $305,700

$t=2017-2012$

$=5$

$236500\times {b}^{5}=305700$

$b}^{5}=\frac{305700}{236500$

${b}^{5}=1.2926$

$b=\sqrt{5}\left\{1.2926\right\}$

$b=1.05267$

Hence, the exponential function is$V\left(t\right)=236500\times {\left(1.05267\right)}^{t}=400000$

$\left(1.05267\right)}^{t}=\frac{400000}{236500$

${\left(1.05267\right)}^{t}=1.691332$

Take logarithm on both sides of the equation:

$t\times \mathrm{log}\left(1.05267\right)=\mathrm{log}\left(1.691332\right)$

$t=\frac{\mathrm{log}\left(1.691332\right)}{\mathrm{log}\left(1.05267\right)}$

$=\frac{0.228229}{0.02229}$

$=10.23$

$\approx 10$

Hence, after 10 years value of home will become $400,000.

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

In 2017, value of home is $305,700

Hence, the exponential function is

Take logarithm on both sides of the equation:

Hence, after 10 years value of home will become $400,000.