The relationship between the height and the diameter of a tree is approximately determined by the equation f (x) = kx3/2, where x is the height in feet, f (x) is the diameter in inches, and k is a constant that depends on the kind of tree you are measuring.
a. A 221 ft British Columbian pine is about 21 in. in diameter. Find the value of k, and use it to express diameter as a function of height.
b. Give the inverse function.
c. Find the diameter of a 300 ft British Columbian pine.
d. What would be the height of a similar pine that is 15 in. in diameter?