The problem can be represented by the the exponential growth formula which is :
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
<span>predicted increase in value per year = 4% =0.04
</span>
<span>∴ r = 1 + 0.04 = 1.04
</span>
<span>for t = 18 years
</span>
∴
<span />
Rounding to the nearest dollar ⇒ ∴ P(t) = <span>564,474
</span>
So, the predicted value of David's home in 18 years = $564,474
So, The correct option is <span>$564,474</span>
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
<span>predicted increase in value per year = 4% =0.04
</span>
<span>∴ r = 1 + 0.04 = 1.04
</span>
<span>for t = 18 years
</span>
∴
Rounding to the nearest dollar ⇒ ∴ P(t) = <span>564,474
</span>
So, the predicted value of David's home in 18 years = $564,474
So, The correct option is <span>$564,474</span>