Question

For certain species of tree, the height h, in meters, is approximated by the diameter d, in centimeters, using the formula (in the picture below). Which is closest to the diameter of a 45-meter tall tree of this species?

Answer 1

Let's rearrange the equation using algebra such that the variable d is isolated. The solution is as follows:

h = 1.75 ⁵√d⁴
h = 1.75[d^(4/5)]
d^(4/5) = h/1.75
d = ⁵√(h/1.75)⁴

When h = 45,
d = ⁵√(45/1.75)⁴
d = 13.43 cm