The problem can be represented by the the exponential growth formula which is :
[tex]P(t) = A * r^{t} [/tex]
Where: t ⇒ time , A ⇒ initial amount , r ⇒ rate of increase
P(t) ⇒ predicted amount at the end of t.
For the given problem:
initial amount = A = $278,640
predicted increase in value per year = 4% =0.04
∴ r = 1 + 0.04 = 1.04
for t = 18 years
∴ [tex]P(t) = A * r^{t} =278,640 * 1.04^{18}=\framebox{564,473.5}[/tex]
Rounding to the nearest dollar ⇒ ∴ P(t) = 564,474
So, the predicted value of David's home in 18 years = $564,474
So, The correct option is $564,474
