Final answer:
The value of the yacht in respect to the original price is 2.1052P.
Step-by-step explanation:
To find the value of the yacht in respect to the original price, we need to apply the percentage changes to the original price. Let's assume the original price is represented by P.
First, the value of the yacht increases by 78% in the first year, so the price becomes (P + 0.78P) = 1.78P.
In the second year, the value increases by 34%, so the price becomes (1.78P + 0.34*1.78P) = 2.39P.
In the third year, the value decreases by 12%, so the price becomes (2.39P - 0.12*2.39P) = 2.1052P.
Therefore, the value of the yacht in respect to the original price is 2.1052P.