proportionality A〖∝ L〗^3
A 20-foot sailboat estimated cost is $10,000. So what would the estimated cost be for a similar 40-foot boat?
If A is the cost, and is proportional to L^3, and L is the length of the boat, then
A = kL
Find k:
10000 = k*20^3 = 8000k
k = 1.25
Now we have the formula
A(L) = 1.25 L^3
A(40) = 1.25 * 40^3 = 1.25 * 64000 = 80,000
Makes sense. If the length scales by a factor of 2, the cost scales by a factor of 2^3 = 8.