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

Consider the following exponential function of value of the home:
${\displaystyle V\left(t\right)=a{b}^t}$
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
${\displaystyle a{b}^0=236500}$
${\displaystyle a=236500}$
In 2017, value of home is $305,700
${\displaystyle t=2017-2012}$
${\displaystyle =5}$
${\displaystyle 236500\times b^5=305700}$
${\displaystyle b^5=\frac{305700}{236500}}$
${\displaystyle b^5=1.2926}$
${\displaystyle b=\sqrt{5}\left\{1.2926\right\}}$
${\displaystyle b=1.05267}$
Hence, the exponential function is ${\displaystyle V\left(t\right)=236500\times {\left(1.05267\right)}^t=400000}$
${\displaystyle {\left(1.05267\right)}^t=\frac{400000}{236500}}$
${\displaystyle {\left(1.05267\right)}^t=1.691332}$
Take logarithm on both sides of the equation:
${\displaystyle t\times \log \left(1.05267\right)=\log \left(1.691332\right)}$
${\displaystyle t=\frac{\log \left(1.691332\right)}{\log \left(1.05267\right)}}$
${\displaystyle =\frac{0.228229}{0.02229}}$
${\displaystyle =10.23}$
${\displaystyle \approx 10}$
Hence, after 10 years value of home will become $400,000.