At the beginning of $2000,$ Russell's house was worth $244$ thousand dollars and Juan's house was worth $116$ thousand dollars. At the beginning of $2003,$ Russell's house was worth $182$ thousand dollars and Juan's house was worth $150$ thousand dollars. Assume that the values of both houses vary at exponential rates.

a$.$ Write a function $f$ that determines the value of Russell's house $($in thousands of dollars$)$ in terms of the number of years $t$ since the beginning of $2000.$

$f(t)=1$

b$.$ Write a function $g$ that determines the value of Juan's house $($in thousands of dollars$)$ in terms of the number of years $t$ since the beginning of $2000.$

$g(t)=$

c$.$ How many years after the beginning of $2000$ will Russell's and Juan's houses have the same value?

years