EXPLANATION :
Note that the Exponential growth or decay function is :
[tex]y=A(1+r)^t[/tex]
where y = final value
A = initial value
(1 + r) = growth or decay factor
r = rate of growth or decay
t = time in years
The function is growth if the expression (1 + r) is greater than 1 and it is decay if (1 + r) is less than 1.
From the problem, we have :
[tex]v(t)=344500(0.81)^t[/tex]
where v(t) is the final value.
The initial value of the house is $344500
Since the value of the parenthesis is 0.81 which is less than 1, the function is decay
Let's solve the rate of decay (r) :
[tex]\begin{gathered} 1+r=0.81 \\ r=0.81-1 \\ r=-0.19 \end{gathered}[/tex]
This will be the rate of change each year.
The rate of change is -19% each year.
